Chapter 6

0 Partnership Rule 1

rem: In a group of npersons invested different amount different period then their profit ratio is & 2 : C r 3 :DtA :...: Xtn first person invested amount A for tt period, second

invested amount B for t2 period and so on.

trative Examples Three partners A, B and C invest Rs 1600, Rs 1800 and Rs 2300 respectively in business. How should they divide a profit of Rs 193 8? The profit should be divided in the ratios of the capi-tals, i.e. in the ratio 16 :18 :23. Now, 16+18 + 23 = 57

16 As share = ofRs 1938 = Rs 544

B'sshare= ofRs 1938 =Rs 612

C's share = ofRs 1938 =Rs 782

A, B and C enter into partnership. A advances Rs 1200 for 4 months, B Rs 1400 for 8 months, and C Rs 1000 for 10 months. They gain Rs 585 altogether. Find the share of each. v Rs 1200 in 4 months earns as much profit as Rs 1200 x 4 or Rs 4800 in 1 month. Rs 1400 in 8 months earns as much profit as Rs 1400 x 8 or Rs 11200 in 1 month. Rs 1000 in 10 months earns as much profit as Rs 1000 x 10orRsl0,000inl month. Therefore, the profit should be divided in the ratio of 4800,11,200 and 10,000 i.e. in the ratios of 12,28 and 25. Now, 12 + 28 + 25 = 65

1 2 cot A's share = ~-x585 = RS 108

65 28

B's share = x585 =RS252 65

C's share = 25 65

x585 =RS225

Note: In compound partnership, the ratio of profit is directly proportional to both money and time, so they are multiplied together to get the corresponding shares in the ratio of profits.

Ex. 3: A starts a business with Rs 2,000. B joins him after 3 months with Rs 4,000. C puts a sum ofRs 10,000 in the business for 2 months only. At the end of the year the business gave a profit of Rs 5600. How should the profit be divided among them? Ratio of their profits (As: B's: C's) = 2x12: 4x9:10x2

= 6 : 9 : 5 Now,6 + 9 + 5 = 20

5600 r Then A's share =^x6 = R s 1680

Soln:

Ex.4:

Soln:

20 5600

B's share = - r ^ x 9 =Rs2520

C's share =

20

5600 ~20~

x5 = R S HOO

A and B enter into a speculation. A puts in Rs 50 and B puts in Rs 45. At the end of 4 months A withdraws half his capital and enters with a capital ofRs 70. At the end of 12 months, in what ratio will the profit be divided? A's share : B's share : C's share

= 50x4 + x8:45x6 + x6:70x6 2 2

=400:405:420 = 82:81:84 Therefore, the profit will be divided in the ratio of 80 : 81:84. Now, you must have understood both simple part-nership and compound partnership. The formula for compound partnership can also be written as

A's Capital* A's Time in partnership _ A's Profit B's Capital xB's Time in partnership B's Pr ofit

126 P R A C T I C E B O O K ON Q U I C K E R MATH

The above relationship should be remembered be-cause it is used very often in some types of question.

Exercise 1. Three friends A, B and C started a business by invest-

ing a sum of money in the ratio of 5 :7 :6. After 6 months C withdraws half of his capital. If the sum invested by 'A is Rs 40,000, out of a total annual profit ofRs 33,000 C's share will be [BSRB Hyderabad PO, 1999] a) Rs 9,000 b)Rs 12,000 c)Rs 11,000 d)Rs 10,000

2. Mr Shivkumar started a business, investing Rs 25000 in 1996. In 1997 he invested an additional amount ofRs 10000 and Mr Rakesh joined him with an amount ofRs 35000. In 1998, Mr Shivkumar invested another addi-tional amount ofRs 10000 and Mr Suresh joined them with an amount ofRs 35000. What will be Rakesh's share in the profit ofRs 150000 earned at the end of three years from the start of the business in 1996?

[SBI PO Exam, 2001] a) Rs 70000 b)Rs 50000 c)Rs 45000 d)Rs 75000

3. A starts a business by investing Rs 500, B joins him after two months by investing Rs 400 and C joins them after 6 months by investing Rs 800. I f the annual profit is Rs 444, find the profit of C. a)Rsl80 b)Rsl20 c)Rsl44 d)Rsl48

4. A, B and C enter into a partnership. A invests Rs 4000 for the whole year, B puts in Rs 6000 at the first and increasing to Rs 8000 at the end of 4 months, whilst C puts in at first Rs 8000 but withdraw Rs 2000 a the end of 9 months. Find the profit of A at the end of year, if the total profit is Rs 16950. a)Rs3600 b)Rs6600 c)Rs6750 d)Rs6300

5. A, B and C go into business as partners and collect a profit ofRs 1000. If A's capital: B's capital = 2:3 and B's capital : C's capital = 2:5, find the share of the profit which goes of C. a)Rsl60 b)Rs240 c)Rs500 d)Rs600

6. Two partners put Rs 1000 and Rs 1500 into a business. How should a profit ofRs 336.70 be divided? a) Rsl 34.68, Rs 202.02 b)Rs 136, Rs 200.70 c)Rs 132.68, Rs 204.2 d) Rsl 36, Rs 202.2

7. Three partners A, B and C invest Rs 2000, Rs 2500 and Rs 1100 respectively in a business. If the total profit is Rs 562.80, find the share of A in the profit. a)Rs201 b)Rs205 c)Rs204 d)Rs208

8. Three men A, B and C subscribe Rs 4700 for a business. A subscribes Rs 700 more than B and B Rs 500 more than C. How much will C receive out of a profit ofRs 423? a)Rsl35 b)Rsl98 c)Rs90 d)Rsl90

9. A is a working and B a sleeping partner in a business. A

puts in Rs 5000 and B puts in Rs 6000. A receives 12-^ %

of the profits for managing the business, and the rest divided in proportion to their capitals. What does eacfc get out of a profit ofRs 880? a)Rs350,Rs420 b)Rs460,Rs350 c)RsllO,Rs420 d)Rs460,Rs420

10. A starts a business with Rs 1000. B joins him after i months with Rs 4000. C puts a sum of Rs 5000 for 4 months only. At the end of the year the business gave i profit of Rs 2800. How should the profit be divided among them? a) Rs600,.Rs 1200, Rs 1000 b) Rs800, Rs 600, Rs 1400 c) RslQ00,Rs 1200, Rs 600 d) Rs 1200, Rs 600, Rs 1000

11. A and B enter into a partnership for a year. A contri utes Rs 3000 and B Rs 4000. After 8 months they adi C, who contributes Rs 4500. If B withdraws his contri tion after 6 months, how would they share a profit of 1000 at the end of the year? a) Rs 250, Rs 200, Rs 550 b) Rs 150, Rs 200, Rs 650 c) Rs 375, Rs 250, Rs 375 d) Data inadequate

12. A, B and C enter into a partnership. A advances o third of the capital for one-third of the time. B con* utes one-sixth of the capital for one-third of the time contributes the remaining capital for the whole time. H should they divide a profit ofRs 1200. a) Rs 300, Rs 200, Rs 700 b) Rs 200, Rs 100, Rs 900 c) Rs 200, Rs 200, Rs 800 d) Rs 150, Rs 250, Rs 800

13. A and B entered into partnership with Rs 700 and Rs

2 respectively. After 3 months A withdrew of his st

3 but after 3 months more he put back of what he

withdrawn. The profits at the end of the year are Rs how much of this should A receive? a)Rs633 b)Rs336 c)Rs663 d)Rs366

14. A and B start a business, A puts in double of what!

1 puts. A withdraws of his stock at the end of 3 mo

i L but at the end of 7 months puts back of what he a

taken out, when B takes out of his stock. A recej 4

Rs 300 profits at the end of the year, what does B J ceive? a)Rsl08 b)Rs272 c)Rsl92 d)Rs208

15. A, B, C pasture in the same field. A has in it 10 oxenl 7 months, B has 12 oxen for 5 months and C has 15 oJ for 3 months. The rent is Rs 17.50. How much of the J

rtnership

should each pay? a) Rs 7, Rs 6, Rs 4.50 b) Rs 6, Rs 8, Rs 3.50 c)Rs7,Rs5,Rs5.50 d)Rs8,Rs5,Rs4.50 Vimla and Sufjeet started a shop jointly by investing Rs 9000 and Rs 10500 respectively. After 4 months Jaya joined them by investing Rs 12500 while Surjeet with-drew Rs 2000. At the end of the year there was a profit of Rs 4770. Find the share of Jaya. a)Rsl620 b)Rsl650 c) Rs 1500 d) Data inadequate

x (LIC1991) A and B enter into partnership investing Rs 12000 and Rs 16000 respectively. After 8 months, C also joins the business with a capital ofRs 15000. The share of C in a profit ofRs 45600 after 2 years will be: a)Rs 12000 b)Rs 14400 c)Rs 19200 d)Rs21200

(Central Excise 1988) A and B entered into a partnership investing Rs 16000 and Rs 12000 respectively. After 3 months, A withdrew Rs 5000 while B invested Rs 5000 more. After 3 more months, C joins the business with a capital fo Rs 21000. The share of B exceeds that of C, out of a total profit of Rs 26400 after one year, by a)Rsl200 b)Rs2400 c)Rs3600 d)Rs4800

(Central Excise, 1989) Suresh invested Rs 12000 in a shop and Dinesh joined him after 4 months by investing Rs 7000. If the net profit after one year be Rs 13300, Dinesh's share in the profit

profit is a)Rsl000 b)Rs600 c)Rs800 d)Rs400

(Asstt. Grade, 1987) 24. A and B enter into partnership investing Rs 12000 and

Rs 16000 respectively. After 8 months, C also joins the business with a capital ofRs 15000. The share of C in a profit ofRs 45600 after 2 years will be a) Rs 12000 b)Rs 14400 c)Rs 19200 d)Rs21200

(Central Excise & I. Tax, 1988) 25. Kishan and Nandan started a joint firm. Kishan's invest-

ment was thrice the investment of Nandan and the pe-riod of his investment was two times the period of in-vestment of Nandan. Nandan got Rs 4000 as profit for his investment. Their total profit if the distribution of profit is directly proportional to the period and amount, is a) Rs 24000 b)Rs 16000 c)Rs 28000 d)Rs 20000

(BankPO Exam, 1989)

Answers 1. a; Hint: Sum invested by A, B and C is in the ratio of

5x 12:7* 12:6x6 + 3 x6 or, 60:84:54 or 10:14:9

9 .-. share of C= x 33000 =R S 9,000

2. b; Hint: Ratio of their investments =25,000 x 1 +35000 * 1 +45000 x 1:35000 x 2:35000 x 1 =3:2:1

a)Rs9576 b)Rs4900 c)Rs8400 d) None of these (SBI PO Exam, 1987)

Ashok invests Rs 3000 for a year and Sunil joins him A ith Rs 2000 after 4 months. After the year they receive i return ofRs 2600. Sunil's share is a)Rs800 b)Rsl000 c)Rs750 d)Rs900

(Railway Recruitment Board, 1991) Jagmohan, Rooplal and Pandeyji rented a video cassette for one week at a rent ofRs 350. If they use it for 6 hours, 10 hours and 12 hours respectively, the rent to be paid by Pandeyji is a)Rs75 b)Rsl25 c)Rs35 d)Rsl50

(BankPO Exam, 1988) Manoj got Rs 6000 as his share out of the total profit of Rs 9000 which he and Ramesh earned at the end of one year. If Manoj invested Rs 20000 for 6 months, whereas Ramesh invested his amount for the whole year, the amount invested by Ramesh was a) Rs 60000 b)Rs 10000 c)Rs 40000 d)Rs5000

(BankPO Exam, 1991) A, B and C invest Rs 2000, Rs 3000 and Rs 4000 in a business. After one year A removed his money. B and C continued the business for one more year. If the net profit after 2 years be Rs 3200, then A's share in the

Rakesh's share = - x 150000 = Rs 50000. 6

3. c 4. a; Hint: A's investment for 12 months = Rs 4000 x 12

= Rs 48000 B's investment (Rs 6000 for 4 months and Rs 8000 for 8 months) = (Rs 6000 x 4 + Rs 8000 x 8) = Rs 88000 C's investment (Rs 8000 for 9 months and Rs 6000 for 3 months) = (Rs 8000 x 9 + Rs 6000 x 3) = Rs 90,000. Ratio of their incomes = A : B : C

= 48000:88000:90000 = 48:88:90 = 24:44:45

5. d; Hint: A's capital: B's capital = 2:3

, 5 , 15 Also, B's capital: C's capital = 2:5= ^ " ~*T

.-. A's capital: B's capital: C's capital =2 :3 : 15 2

4:6:15 Since 4 + 6 + 5 = 25

.-. A's share of the profit = x R s 1000 = Rs 160

6

B's share of the profit = x R s 1000 = Rs 240

128 P R A C T I C E B O O K ON Q U I C K E R MATHS

15

C's share of the profit = x Rs 1000 = Rs 600

6. a 7. a 8.c 9. d; Hint: The amount which A receives for managing

1 1 = 12-% ofRs880= - ofRs880 = Rs 110

2 8 The amount left to be divided in the ratio of 5 : 6

= Rs880-RsllO = Rs770 Now, A's share = ofRs 770 = Rs 350

B's share = yy ofRs 770 = Rs 420

.-. A's total share = Rs 350 + Rs 110 = Rs 460 Note: A working partner is one who manages the business.

A sleeping partner is one who provides capital but doesnot attend to the business.

lO.a 11.c 12.b 13. d; Hint: Ratio of profits of A and B are

A's profit: B's profit = 700x3+ 500 x 3 + 620 x 6:600 x 12 = 2100+1500 + 3720:7200 = 7320:7200 = 61:60

726 726 , , .-. A's share in profit = * o 1 = - x 61

60 + 61 121 = 6x61=Rs366

14. a; Hint: A's profit: B's profit

4x . 14x _ _ 3x , = 2xx3 + x4 + x5: xx7 + x5

3 9 4 r 16x 70x 15x 172x 43x

= 6x + + : 7x + = : 3 9 4 9 4

= 16:9 [We suppose that A puts Rs 2x and B puts Rs x in the business].

15. a 16. c 17. a 18. c; Hint: Ratio of capitals of A, B and C

= (16000 x 3 +11000 x 9): (12000 x 3 +17000 x 9): (21000 x6) = 7:9:6

B's share = Rs (26400x^ "j =Rs 10800

C's share = Rs [ 2 6 4 0 0 > < ^ = Rs 7200

,-, B's share exceeds C's share by Rs 3600 19. d 20. a 21. d; Hint: Ratio of rents = 6:10:12 = 3:5:6

.-. Pandeyji's share of rent = Rs 350x-14

22. d 23. d 24. a 25. c; Hint: Let Nandan's investment be Rs x and y months.

Then, Kishan's investment is Rs 3x for 2y months .-. Ratio of their investments = xy: 6xy =1:6 Nandan's share = Rs 4000 So, Kishan's share = Rs 24000 .-. Total profit = Rs 28000

Rule 2 Theorem: The formula for compound partnership can a be written as

A' s Capital xA's Time in partnership A's Profit B'sCapitalxB's Time in partnership B's Profit

Illustrative Examples Ex. 1: A began a business with Rs 450 and was joined aft

wards by B with Rs 300. When did B join if the pro at the end of the year were divided in the ratio 2 : 1

Soln: Suppose B joined the business for x months. Then using the above formula, we have 450x12 2

or, 300x2* = 450x12 300xx 1 450x12

9 months. 2x300 Therefore, B joined after (12 - 3) = 3 months.

Ex.2: A and B rent a pasture for 10 months. A puts in 1 cows for 8 months. How many can B put in for remaining 2 months, if he pays half as much again A?

Soln: Suppose B puts in x cows. 1 3

The ratio of A's and B's rents = 1:1 + = 1: = 2 2 2

Then, 100x8 100x8x3

or,:c= :: = 600 xx2 3 2x2

Ex. 3: A and B enter into a partnership with their capitals the ratio 7 : 9. At the end of 8 months, A withdr his capital. If they receive the profits in the ratio 8 find how long B's capital was used.

Soln: Suppose B's capital was used for x months. Foil 7x8 8

ing the above rule, we have, 9xx 9 7x8x9 8

or, x = = = 7 \

= Rs 150

8x9 9 Therefore, B's capital was used for 7 months.

Exercise 1. A began a business with Rs 400 and was joined af

wards by B with Rs 240. When did B join if the profi the end of the year were divided in the ratio 4:1? a) 5 months b) 8 months c) 6 months d) 10 months

Partnership

2. A began a business with Rs 300 and was joined after-wards by B with Rs 150. When did B join if the profits at the end of the year were divided in the ratio 3:1? a) 4 months b) 6 months c) 8 months d) 5 months

3. A began a business with Rs 550 and was joined after-wards by B with Rs 330. When did B join if the profits at the end of the year were divided in the ratio 10:3? a) 5 months b) 6 months c) 9 months d) 3 months

4. A and B hire a meadow for 6 months. A puts in 21 cows for 4 months, how many can B put in for the remaining 2

5 months, if he pays of what A pays?

a) 20 b)40 c)35 d)30 5. A and B rentapasture for 12 months. A puts in 120 cows

for 9 months. How many can B put in for the remaining 3 1

months, if he pays as much again as A? a) 840 b)480 c)460 d)640

6. A and B rent a pasture for 12 months. A puts in 3 50 oxen for 5 months. How many can B put in for the remaining 7

2 months, if he pays as much again as A? a) 530 b)350 c)450 d)600

". A and B enter into a partnership with their capitals in the ratio 5 : 7. At the end of 6 months, A withdraws his capital. If they receive the profits in the ratio 6 : 7, find how long B's capital was used? a) 5 months b) 7 months c) 3 months d) 9 months

8. A and B enter into a partnership with their capitals in the ratio 3 : 5. At the end of 4 months, A withdraws his capital. If they receive the profits in the ratio 4 : 5, find how long B's capital was used? a) 2 months b) 5 months c) 4 months d) 3 months

; A and B enter into a partnership with their capitals in the ratio 5 : 9. At the end of 8 months, A withdraws his capital. If they receive the profits in the ratio 4 : 9, find how long B's capital was used? a) 10 months b) 9 months c) 8 months d) 4 months

.0 A started a business by investing Rs 2700. After some-time B joined him by investing Rs 2025. At the end of one year, the profit was divided in the ratio 2:1. After how many months did B join the business?

[UDC Exam, 1984] a) 4 months b) 6 months c) 3 months d) 2 months

Answers 2.c 3.b 4.d 5.b 6.b 7. a

t d 9. a ! 0. a; Hint: Let 'B'joined after 'x' months, then applying the

2700x12 _2 given formula, we have 2 0 25x(12-x) " 1

\ *=4

Rule 3 If investments are in the ratio ofa : b : c and the timing of their investments in the ratio of x : y : z then the ratio of their profits are in the ratio of ax: by: cz-

Illustrative Example Ex.: A, B and C invested capitals in the ratio 2 : 3 : 5; the

timing of their investments being in the ratio 4 : 5 : 6 . In what ratio would their profit be distributed?

Soln : We should know that if the three investments be in the ratio a: b : c and the duration for their investments be in the ratio x: y: z, then the profit would be distrib-uted in the ratio ax : by : cz. Thus, following the same rule, the required ratio

= 2 x 4 : 3 x 5 : 5 x 6 = 8:15:30

Exercise 1. A, B and C invested capitals in the ratio 1 : 2 : 3; the

timing of their investments being in the ratio 1 :2 : 3. In what ratio would thier profit be distributed? a ) 3 : 2 : l b ) l : 2 : 3 c ) l : 4 : 9 d ) 9 : 4 : l

2. A, B and C invested capitals in the ratio 2 : 5 : 7; the timing of their investments being in the ratio 3 : 4 : 5. In what ratio would thier profit be distributed? a)2:10:15 b)15:10:2 c)6:20:35 d)6:20:15

3. A, B and C invested capitals in the ratio 3 : 5 : 9; the timing of their investments being in the ratio 2 : 3 : 1. In what ratio would thier profit be distributed? a)6:15:8 b )3 :5 :2 c)2:5:3 d)2:3:5

4. A, B and C invested capitals in the ratio 7 : 6 : 5; the timing of their investments being in the ratio 4 : 7 : 9. In what ratio would thier profit be distributed? a)9:14:15 b)28:42:45 c) 15:14:9 d)28:24:54

5. A, B and C invested capitals in the ratio 3 : 4 : 9; the timing of their investments being in the ratio 9 : 6 : 7. In what ratio would thier profit be distributed? a)9:8:21 b)27:25:63 c)27:24:36 d)9:8:12

Answers l.c 2.c 3.c 4.b 5.a

Rule 4 Theorem: If investments are in the ratio a:b:c and profits

p q r in the ratio p: q: r, then the ratio of time = .

e n J a b c Illustrative Example Ex.: A, B and C invested capitals in the ratio 5 :6 : 8. At the

end of the business term, they received the profits in the ratio 5 :3 : 12. Find the ratio of time for which they contributed their capitals.

Soln: Using the above formula, we have

the required ratio ; 5 3 12 1 3 - : - : = 1: : = 2:1:3 5 6 8 2 2

130 P R A C T I C E B O O K ON Q U I C K E R MATHS Partr.

Exercise 1. A, B and C invested capitals in the ratio 6:9:10. At the

end of the business term, they received the profits in the ratio 2:3 :5. Find the ratio of time for which they contrib-uted their capitals. a)2:2:3 b) 12:27:50 c) 1:1:2 d)2:3:3

2. A, B and C invested capitals in the ratio 1 : 2 : 3. At the end of the business term, they received the profits in the ratio 1:2:3. Find the ratio of time forwhich they contrib-uted their capitals. a)1:1:1 b) 1:2:3 c) 1:4:9 d) Can't be possible

3. A, B and C invested capitals in the ratio 4 : 5 : 6. At the end of the business term, they received the profits in the ratio 2:3:4. Find the ratio of time for which they contrib-uted their capitals.

. a)6:5:8 b)6:5:9 c)10:12:9 d) 12:10:9 4. A, B and C invested capitals in the ratio 4 : 6 : 9. At the

end of the business term, they received the profits in the ratio 2:3:5. Find the ratio of time for which they contrib-uted their capitals. a) 1:1:9 b)2:2:9 c)10:10:9 d)5:5:9

5. A, B and C invested capitals in the ratio 7 : 3 : 2. At the end of the business term, they received the profits in the ratio 2:3:7. Find the ratio of time for which they contrib-uted their capitals. a)49:41:14 b)49:14:41 c)49:14:4 d)49:41:4

Answers La 2.a 3.d 4.c 5.c

Rule 5 Theorem: Three partners invest their capitals in a busi-ness. If the ratio of their periods of investments are t\\t2: /3 and their profits are in the ratio of a: b: c, then the

capitals will be in the ratio of ; . h ti

Illustrative Example Ex.: A, B and C invest their capitals in a business. If the

ratio of their periods of investments are 2 : 3 : 4 and their profits are in the ratio of 4:9: 8. Find the ratio in which the investments are made by A, B and C.

Soln: Applying the above rule, we have 8 T =2:3 :2 -

4 9 the required answer = :

Exercise 1. A, B and C invest their capitals in a business. If the ratio

of their periods of investments are 1 : 2 : 3 and their profits are in the ratio of 2 : 3 : 1. Find the ratio in which the investments are made by A, B and C. a)12:9:2 b)2:9:12 c )6 :3 : l d) 1:3 :6

2. A, B and C invest their capitals in a business. If the ratio of their periods of investments are 2 : 3 : 4 and their profits are in the ratio of 4 : 3 :2. Find the ratio in which the investments are made by A, B and C. a) l :2:4 b )4 :2 : l c )3 :2 : l d)4:2:3

3. A, B and C invest their capitals in a business. If the ratio of their periods of investments are 2 : 3 : 6 and their profits are in the ratio of 4 : 5 : 6. Find the ratio in which the investments are made by A, B and C. a)9:10:12 b)4:5:6 c)8:5:12 d)6:5:3

4. A, B and C invest their capitals in a business. If the ratio of their periods of investments are 7 : 3 : 5 and their profits are in the ratio of 2 : 1 :2. Find the ratio in which the investments are made by A, B and C. a)30:35:42 b)7:6: 10 c)42:30:35 d)42:25:35

Answers l.a 2.b 3.d 4.a

Rule 6 X

Theorem: A, B and C are partners. A receives ~ of the

profit and B and C share the remaining profit equally. If A's income is increased by Rs 'A' when the profit rises from

P% to Q%, then the capital invested by A is ( n 100x/fA

Rs Q-P

and the capital invested by B and C is Rs

^100x^1^ x^ Q-P

or A's Capital^

2 J x y'j Illustrative Example

2 Ex.: A, B and C are partners. A receives j of the profit

and B and C share the remaining profit equally. A's income is increased by Rs 220 when the profit rises from 8% to 10%. Find the capitals invested by A, B and C.

Soln: Detail Method: For A's share: (10% - 8%) = Rs 220

100% 220 xl00 =Rs 11000

.'. A's capital = Rs 11000

For B's & C's share: y =11000

3 ' 5

1000 x3 =R S 16500

I

Partnership

.-. B's and C's capitals are Rs 8250 each. Quicker Method: Applying the above rule, we have,

100x220 A's capital = - = Rs 11000

10-

B's and C's capitals:

100x220 , 2 x 1

10-8 I 5

: Rs 8250 each.

Exercise

2 A, B and C are partners. A receives of the profit and

B and C share the remaining profit equally. A's income is increased by Rs 240 when the profit rises from 10% to 15%. Find the capitals invested by B and C. a)Rs2400 b)Rsl200 c)Rs4800 d)Rs6000

5 _ A, B and C are partners. A receives of the profit and

8 B and C share the remaining profit equally. A's income is increased by Rs 450 when the profit rises from 4% to 9%. Find the capitals invested by B and C. a)Rs3366 b)Rs 1687.5 c)Rs3475 d)Rs3466

9 1 A, B and C are partners. A receives of the profit and

B and C share the remaining profit equally. A's income is increased by Rs 270 when the profit rises from 12% to 15%. Find the capitals invested by B and C. a)Rs5000 b)Rsl000 c)Rs500 d)Rsl500

5 A, B and C are partners. A receives of the profit and B and C share the remaining profit equally. A's income is increased by Rs 225 when the profit rises from 8% to 13%. Find the capitals invested by B and C. a)Rsl000 b)Rs2000 c)Rs2500 d)Rs950

' ]r 10 p. A, B and C are partners. A receives of the profit and

B and C share the remaining profit equally. A's income is increased by Rs 550 when the profit rises from 11% to 13%. Find the capitals invested by B and C. a)Rs4125 b)Rs4215 c)Rs4251 d)Rs4512

Aaswers Ld 2.b 3.c 4. a 5. a

Rule 7 Tmv partners invest Rs x and Rsy respectively in a business mmi agree that P% of the profit should be divided equally B * ien them and the remaining profit is to be treated as mmerest on capital If one partner gets RsXmore than the

then to find the total profit made in the business we m*ct the following steps.

Step I: First find the ratio of the profit ie Rs x : Rs y = A : B (say)

Step II: Now, apply this formula to calculate the total profit.

Total profit = RsAr ( ioo YA + B \\00-PXA-B J

Illustrative Example Ex.: Two partners invest Rs 125,000 and Rs 85,000 respec-

tively in a business and agree that 60% of the profit should be divided equally between them and the re-maining profit is to be treated as interest on capital. If one partner gets Rs 300 more than the other, find the total profit made in the business. Detail Method: The difference counts only due to the 40% of the profit which was distributed according to their investments. Let the total profit be Rs x. Then 40% of x is distributed in the ratio 125,000 : 85,000=25:17 Therefore, the share of the first partner

Soln:

= 40% oft

= 40% of*

25 25 + 17

25^ _ 40x^25^| _ 5x ~2A ^2) 100 ^42

and the share of the second partner

\l\_\lx 105

Now, from the question,

= 40% oft

the difference in share = 5x \lx 2T~T05

= 300

or, x(25-17)_

105

300x105

300

= Rs 3937.50 5

Quicker Method: Applying the above rule, we have, Step I: The ratio of profit = 125,000:85,000 = 25 :17

Step II: total profit = 3'

= Rs3937.50 cm

Exercise 1. Two partners invest Rs 24750 and Rs 16500 respectively

in a business and agree that 20% of the profit should be divided equally between them and the remaining profit is to be treated as interest on capital. If one partner gets Rs 400 more than the other, find the total profit made in


the business. a)Rs5000 b)Rs2500 c)Rs3500 d)Rs4500

2. Two partners invest Rs 26000 and Rs 16250 respectively in a business and agree that 40% of the profit should be divided equally between them and the remaining profit is to be treated as interest on capital. If one partner gets Rs 450 more than the other, find the total profit made in the business. a)Rs3250 b)Rs3520 c)Rs3230 d)Rs3200

3. Two partners invest Rsl7000 andRsl3000 respectively in a business and agree that 75% of the profit should be divided equally between them and the remaining profit is to be treated as interest on capital. If one partner gets Rs 532 more than the other, find the total profit made in the business. a) Rs 16960 b)Rs 14960 c)Rs 16950 d)Rs 15960

4. Two partners invest Rs 6280 and Rs 3768 respectively in a business and agree that 30% of the profit should be divided equally between them and the remaining profit is to be treated as interest on capital. If one partner gets Rs 700 more than the other, find the total profit made in the business. a)Rs4000 b)Rs3800 c)Rs4125 d)Rs4500

5. Two partners invest Rs 87000 and Rs 72500 respectively in a business and agree that 25% of the profit should be divided equally between them and the remaining profit is to be treated as interest on capital. I f one partner gets Rs 240 more than the other, find the total profit made in the business. a)Rs3250 b)Rs3520 c)Rs3620 d)Rs3720

Answers l.b 2. a 3.d 4. a 5.b

Rule 8 Two partners A and B invests in the ratio x :y in a business. IfP% of the total profit goes to charity and A's share is Rs

100 Y y X, then the total profit is given by Rs X I _ p 1 1 +

Illustrative Example Ex.: A and B invested in the ratio 3 :2 in a business. If 5%

of the total profit goes to charily and A's share is Rs 855, find the total profit.

Soln: Detail Method: Suppose the total profit is Rs 100. Then Rs 5 goes to charity. Now, Rs 95 is divided in the ratio 3:2.

95 , A's share = T ~ x 3 =RS57 3 + 2 But we see that A's actual share is Rs 855.

ioo s ~57~ Actual total profit =855

Quicker Method: Applying the above rule, we have 100 Y3 + 2N

the total profit : 855 100-5

= 855 100 95 - | =Rs 1500.

Exercise 1. A and B invested in the ratio 5 :3 in a business. If 10% of

the total profit goes to charity and A's share is Rs 900, find the total profit. a)Rsl600 b)Rsl400 c)Rsl500 d)Rsl800

2. A and B invested in the ratio 4 :9 in a business. If 8% of the total profit goes to charity and A's share is Rs 460, find the total profit. a)Rs2625 b)Rs2526 c)Rsl526 d)Rsl625

3. A and B invested in the ratio 5 : 7 in a business. If 7% of the total profit goes to charity and A's share is Rs 1860, find the total profit. a)Rs8400 b)Rs4600 c)Rs4850 d)Rs4800

4. A and B invested in the ratio 5 :4 in a business. If 4% of the total profit goes to charity and A's share is Rs 480, find the total profit. a)Rs900 b)Rs800 c)Rs850 d)Rs950

5. A and B invested in the ratio 5 :2 in a business. If 12% of the total profit goes to charity and A's share is Rs 770, find the total profit. a)Rsl325 b)Rsl235 c)Rsl225 d)Rs2125

Answers La 2.d 3.d 4. a 5c

Rule 9 Formula: The ratio of investments - Ratio of Profits

Illustrative Example Ex.: Three partners altogether invested Rs 114,000 in a

business. At the end of the year, one got Rs 337.50, the second Rs 1125.00 and the third Rs 675 as profit. How much amount did each invest? What is the per-centage of profit?

Soln: The ratio of investments = Ratio of profits = 337.50:1125:675 =3375:11250:6750

Dividing each by 1125, we have the ratio = 3:10:6. 114000 ,

Shares of the partners = Rs -: x 3.

Rs 114000

xlO andRs

3 + 10 + 6

114000 3 + 10 + 6 3 + 10 + 6

or, Rs 18000, Rs 60000 and Rs 36000 The required percentage of profit

x6

Rs1500 337.5 + 1125 + 675 114000

Xl00: 2137.50 1140 = 1.857%

Partnership

Exercise 1. Three partners A, B and C together invested Rs 375000

in a business. At the end of the year, A got Rs 52000, B got Rs 65000 and C got Rs 78000 as profit. How much amount did A invest? a) Rs 100000 b)Rs 125000 c) Rsl 50000 d)Rs 160000

2. Three partners A, B and C together invested Rs 14400 in a business. At the end of the year, A got Rs 1250, B got Rs 2500 and C got Rs 3750 as profit. How much amount did C invest? a)Rs2400 b)Rs4800 c)Rs7200 d)Rs9600

3. Three partners A, B and C together invested Rs 36000 in a business. At the end of the year, A got Rs 4200, B got Rs 7000 and C got Rs 9800 as profit. How much amount did B invest? a)Rs7200 b)Rs 12000 c)Rs 16800 d)Rs 12500

4. Three partners A, B and C together invested Rs 22500 in a business. At the end of the year, A got Rs 2800, B got Rs 8400 and C got Rs 14000 as profit. How much amount did A invest? a)Rs2500 b)Rs7500 c)Rs 12500 d)Rs5000

5. Three partners A, B and C together invested Rs 21600 in a business. At the end of the year, A got Rs 700, B got Rs 800 and C got Rs 900 as profit. How much amount did B and C together invest? a)Rs 15300 b)Rs 13500 c)Rs 14400 d)Rs 16300

6. Three partners A, B, C agree to divide the profit or losses in the ratio 1.50 : 1.75 :2.25. If, in a particular year, they earn a profit ofRs 66000, find the share of B. a) Rs 21000 b)Rs 27000 c)Rs 18000 d)Rs 22000

(LIC1991) 7. X and Y invested in a business. They earned some profit

and divided in the ratio 2:3. If X invested Rs 40, find the money invested by Y. a)Rs20 b)Rs30 c)Rs80 d)Rs60

(Railways 1991) 8. Jayant started a business, investing Rs 6000. Six months

later Madhu joined him, investing Rs 4000. If they made a profit ofRs 5200 at the end of the year, how much must be the share of Madhu? a)Rsl300 b)Rs3900 c)Rs3600 d)Rsl200

(BankPO 1991) 9. Dilip, Ram and Amar started a shop by investing Rs

2700, Rs 8100 and Rs 7200 respectively. At the end of one year, the profit was distributed. I f Ram's share was Rs 3600, theirtotal profit was (BankPO Exam 1988) a) Rs 10800 c)Rs8000

Answers l.a 2.c 3.b 4.a 5.a 6.a 7.d 8. a

b)Rs 11600 d) None of these

9. c; Hint: Ratio of shares of Dilip, Ram and Amar =2700:8100:7200=3:9:8

If Ram's share is Rs 9, total profit = Rs 20 '20

If Ram's share is Rs 3600, total profit = Rs x 3 6 0 0

= Rs8000

Rule 10 Two partners A and B start a business. A puts in Rs 'A' more in the business than B, but B has invested his capital for T2 periods while A has invested his capital for 7j peri-ods. If the share of A is Rs 'a' more than that of B out of the total profits of Rs 'P', then the capital contributed by B is

Rs (P + a)T2 -1 and the capital contributed by A is

given by [Rs A + Capital of BJ.

Illustrative Example Ex.: A puts Rs 600 more in a business than B, but B has

invested his capital for 5 months while A has invested his for 4 months. If the share of A is Rs 48 more than that of B out of the total profits ofRs 528, find the capital contributed by each?

Soln: Detail Method:

B's profit = Rs 528-48

= Rs240

A's profit = Rs 240 + Rs 48 = Rs 288

288

.-. A's profit per month = Rs =Rs72

240 B's profit per month = Rs =Rs48 Now, their capitals are proportional to their profits. .-. A's capital: B's capital = 72 :48 = 3 : 2 .-. I f the difference between their capitals be Re 1, then A's capital is Rs 3 and B's capital is Rs 2. But the actual difference is Rs 600. .-. A's capital = Rs 600 x 3 = Rs 1800 B's capital = Rs 600 x 2 = Rs 1200 Quicker Method: Applying the above rule, we have B's capital

600 600 600 [(528 + 48)5) {(528 - 48)4 J

1 576x5 - 1

= Rsl200 1

480x4

A's capital = Rs 1200 + Rs 600 = Rs 1800.


Exercise 1. A puts Rs 795 more in a business than B, but B has

invested his capital for 6 months while A has invested his for 5 months. If the share of A is Rs 33 more than that of B out of the total profits of Rs 432, find the total capital put in the business. a)Rs2000 b)Rs2790 c)Rs4785 d)Rs7490

2. A puts Rs 550 more in a business than B, but B has invested his capital for 4 months while A has invested his for 3 months. If the share of A is Rs 45 more than that of B out of the total profits of Rs 235, find the capital contributed by A?-a)Rsll20 b)Rs550 c)Rs570 d)Rsl210

3. A puts Rs 375 more in a business than B, but B has invested his capital for 4 months while A has invested his for 8 months. If the share of A is Rs 75 more than that of B out of the total profits ofRs 125, find the capital contributed by B? a)Rs750 b)Rs375 c)Rs735 d)Rs573

4. A puts Rs 768 more in a business than B, but B has invested his capital for 7 months while A has invested his for 4 months. If the share of A is Rs 42 more than that of B out of the total profits ofRs 358, find the capital contributed by B? a)Rs642 b)Rsl400 c)Rs632 d)Rs462

5. A puts Rs 280 more in a business than B, but B has invested his capital for 3 months while A has invested his for 4 months. If the share of A is Rs 55 more than that of B out of the total profits of Rs 245, find the total capital in the business. a)Rsl520 b)Rsl800 c)Rs3320 d) Data inadequate

Answers l.c 2.a 3.b 4.c 5.c

1. Miscellaneous

A, B and C can do a work in 20,25 and 30 days respec-tively. They undertook to finish the work together for Rs 2220, then the share of A exceeds that of B by a)Rsl20 b)Rsl80 c)Rs300 d)Rs600

(Central Excise, 1989) 2. A, B and C contract a work for Rs 550. Together A and B

are to do of the work. The share of C should be

a)Rs400 b)Rs300 c)Rs200 d)Rs 183 1

(Clerical Grade, 1991) 3. A, B and C enter into partnership by making invest-

ments in the ratio 3:5:7. After a year, C invests another Rs 337600 while A withdraws Rs 45600. The ratio of in-vestments then changes to 24:59: 167. How much did A invest initially? a) Rs 45600 b) Rs 96000 c) Rs 141600 d) None of these

(LIC, AAO Exam 1988) 4. Three hikers A, B and C start on a trip with Rs 50 each

and agree to share the expenses equally. If at the end of

the trip, A has Rs 20 left with him, B Rs 30 and C Rs 40, how must they settle then accounts? a) C must pay Rs 10 to A b) A must pay Rs 10 to B c) A must pay Rs 10 to C d) Can't be settled

(ITI1985) 5. A and B invest Rs 3000 and Rs 4000 in a business. A

receives Rs 10 per month out of the profit as a remunera-tion for running the business and the rest of profit is divided in proportion to the investments. If in a year 'A' totally receives Rs 390, what does B receive? a)Rs630 b)Rs360 c)Rs480 d)Rs380

(IAS 1980) 6. A sum of money is to be divided among A, B and C in

the ratio 2 : 3 : 7. If the total share of A and B together is Rs 1500 less than C, what is A's share in it? a) Rs 1000 b) Rs 1500 c) Rs 2000 d) Data inadequate

(BankPO Exam, 1989)

Answers

1 1 1 1. b; Ratio of shares = Ratio of 1 days's work = ' '

= 15:12:10.

.-. A's share = Rs ( ^ 2 2 2 0 x ^ | |

B's share = Rs [ 2 2 2 ! ? * | |

;, A's share exceeds B's share = Rs 180 2. c; Do yourself. 3. c; Let the initial investments of A, B, C be Rs 3x, Rs 5x and

Rs Ix respectively. Then, (3x-45600): 5x: (7x +337600) = 24:59:167

3x- 45600 24 5 x 5 9 x = 47200

.-. A invested initially Rs (47200 * 3) = Rs 141600 4. a; Do yourself. 5. b; Total profit - Remuneration = Balance profit.

This balance profit is divided in proportion to their in-vestments. Balance profit of A _ Investment of A Balance profit of B Investment of B

390-10x12 3000 3 o r ' Balance profit of B ~ 4000 ~ 4

(Since remuneration of A is Rs 10 per month)

, 2 7 0 or, Balance profit of B = 4 x ~ ^ ~ =Rs360 Since B does not get any remuneration, hence B re-ceives Rs 360 at the end of the year.

6.b; 7x-(2x + 3x) = Rs 1500 .-. x = Rs750 .-. A = 2x = Rsl500

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