Qa 10305 simple equations

LINEAR EQUATIONS

QA10305

1.The difference between a two-digit number and the number formed by interchanging its digits is 27.The sum of the digits is 9. Find the product of the digits.(1) 9 (2) 18 (3) 27 (4) 36

QA10305

b”.+“10a is number theof value the “ab”, digits theby drepresente be number digit-2 aIf

“b”. & “a” consider should We digits, discusses question the Whenever

b”.+“10a consider should we number, discusses question the Whenever

a”.+“10b is number theof value the “ab”, digits the reversingby formedNumber

b - a 9 is digits the reversingby formednumber the number digit-2 between difference The

1.The difference between a two-digit number and the number formed by interchanging its digits is 27.The sum of the digits is 9. Find the product of the digits.(1) 9 (2) 18 (3) 27 (4) 36

QA10305

9=b+a

3=b)-(a 27 =b)-(a 9 ⇒

3= b or 6= a3=b - a9=b+a

18=digitsof Product

3= a or 6= b3=a - b9=b+a

18=digitsof Product

(2) Choice

2.How many pairs of values satisfy5x+2y=72.5x+y=3.5?(1)0 (2) 1 (3) Infinite (4) None of these

QA10305

......(2) 3.5= y+2.5x 1).........( 7=2y+5x

equation firstthe iswhich, 7=2y+2,5x by

equation second gMultiplyin

Solutions Infinite

3.If we add three times the first number and four times the second number, the sum obtained is 17. If seven times the second number is reduced from 29, we get five times the first number. Find the sum of the two numbers.(1)6 (2) 5 (3) 7 (4) None of these

......(2) x5=7y- 291).........( 71=4y+3x

......(2) 29=7y+5x1).........( 71=4y+3x

3=x 2=y 5=y+x(3) Choice (2) Choice

4.When you reverse the digits of the number 25, the number increases by 27. How many other two-digit numbers increase by 27 when their digits are reversed?(1)7 (2) 8 (3) 9 (4) 5

QA10305

3=a)-(b⇒27= a)-(b 9 is digits the reversingby formed

number the number digittwo between difference The

numbers 5 - 69 and 4,36,47,581

(4) Choice

5.The difference between a three-digit number and the number formed by reversing its digits is always divisible by(1) 9 (2) 99 (3) 199 (4) 98

c”.+10b+“100a is number theof value the “abc”,

digits theby drepresente be number digit-three aIf

b) - (a 99= Difference

a”.+10b+“100c is digits the

reversingby drepresente be number digit-Three

(2) Choice

QA10305

Squares Perfect consider us etL

ok -36=4)+(2 24,=12-36 2

(3) -Choice- 6= 4)+(2

7. Present age of a father is 6 years more than 3 times the age of his son. After how many years will the father be exactly 3 times his son’s age?(1)5 (2) 10 (3) 3 (4) 4

6. What is the sum of the digits of a two-digit number, which is 12 less than the square of the sum of its digits?(1)9 (2) 7 (3) 6 (4) None of these

81,36,49,64, 25 6,1Number digit 2 a not 4= 12 -61

25≠3)+(1 , 31= 12 -52 2 son hisof age thethrice is man the after of years

number the represent n"" Let

6+s3=mson theof age the be s"" and

man theof age the be m"" Let

)n+s(3=n+mn3+s3=n+6+s3

(3) Choice3=n

QA10305

x -11 = rDenominatox"" be numerator the etL

8.When a fraction is inverted and four is added to the numerator and four is deducted from the denominator of this fraction, the resulting fraction is equal to 10. If the sum of the numerator and denominator of the original fraction is 11, what is the numerator of the original fraction?(1) 2 (2) 4 (3)5 (4) 6

x-11x

= fractionOriginal

10=4-x

4+x-11

10=4-xx-15

40 -x10=x-155=x⇒55=11x

(3) Choice

QA10305

theseof None (4) (3)6 (2)7 (1)9

c)+b+(aof value the Find 8.=3d+c+b and 4=d+b , 6=c+a

32,=4d+c+2b+5aIf 9.

12=d4+c+b2,Adding 8.=3d+c+b & 4=d+b

2=a32=d4+c+b2+a5 ⇒4=c6=c+a ⇒

4=d+b 6=d3+b1=d&3=b 9=c+b+a

(1) Choice

10.Some Sparrows and pigeons are sitting on a wire. Five sparrows fly away leaving behind two pigeons for every sparrow left. After some time 25 pigeons fly away, thus leaving behind three sparrow for every pigeon left. Find the original number of sparrows.(1) 20 (2) 30 (3) 50 (4) 25

p=5)-2(s

)25-p(3=5)-(s

p=10-2s

57-p3=5-s

20=s100=5s57- 30-6s=5-s

57-)10-s2(3=5-s

⇒ (1) Choice

QA1030511.Five years ago, Sunita’s age was four times Lata’s age. Fifteen years from now, Sunita’s age will be twice the age of Lata. What is the sum of their present ages?(1)15 (2)45 (3) 60(4)None of these

12. Kumar's present age is six times the present age of his son. When the son's age becomes 3 times of his present age, what would be the age of Kumar if the son's present age is m years?(1) 3m (2) 8m (3) 2m (4) Cannot be determined

(1)5)........-4(l=5)-(s

5)...(2)1+2(l=15)+(s

15=l⇒l2-50=20⇒ (1)- (2)

45=s)5-15(4=5-s ⇒

60=l+s (3) Choice

3m 8m m 6m

Son Kumar

QA1030513. The difference between a three-digit number and the number formed by reversing its digits is ninety-nine. Further six times the digit in the hundred's is five times the digit in the units place. If the middle digit is '0‘ find the number.(1) 506 (2) 605 (3) 403 (4) 304

14. The cost of 3 apples, 5 mangoes and 3 bananas is Rs.145.Cost of 5 apples, 9 mangoes and 5 bananas is Rs. 225. Find the sum of the cost of one apple, one mango and one banana.(1) Rs. 50 (2) Rs. 35 (3) Rs. 40 (4) Rs. 65

1=c)-(a

6= c and 5=a ⇒ 5c=6a

605 (1) Choice 65= b+m+a Adding,522=5b9m5a1-×(2)

902=6b+m01+6a2×(1)----⇒

⇒

)5.......(222=5b+9m+5a(1)145.......=3b+5m+3a

QA10305

15. A coin-dispensing machine contains one-rupee, two-rupee and five-rupee coins. The total number of coins in the machine is 80 and the total amount is Rs.240. If the number of one-rupee coins and number of two-rupee coins are interchanged, the total amount increases by Rs.5.What is the total number of five-rupee coins in the machine? (1) 50 (2) 70 (3) 35 (4) 20

)5.......(342=5c+a2+b)0.......(242=5c+b2+a

.......(1)08=c+b+a

(4)485.......=10c+3b+3a

)c.......(5-80=b+a

(4)485.......=10c+c)-3(80

35=c245=7c⇒485=7c+240

(3) Choice

QA1030516. A stores officer at Suzuki Corporation has five crates of different but unknown weights each weighing less than 1000 kgs. The clerk weights the crates in pairs. The weights obtained are 1110, 1112, 1113, 1114, 1115,1116, 1117, 1118, 1120 and 1121 kgs. What is the weight, in kgs, of the heaviest crate? (1) 560.1 (2) 562 (3) 564 (4) Cannot be determined

Let wt. of the boxes be W1 < W2 < W3 < W4 < W5

The weights given represent 10 different combinations of weights of 2 boxes.

Each box gets weighed 4 times.

Adding , 4(W1+W2+W3+W4 +W5) =11156

(W1+W2+W3+W4 +W5) =2789

(W1+W2) =1110

(W4+W5) =1121

W3 =558

W3 + W5 =1120 W5 =562

(2) Choice

QA1030517. A farmer has decided to build a wire fence along one straight side of his property. For this, he plans to place several fence-posts at eight-meter intervals, with posts fixed at both ends of the side. After he had bought posts and wire, he found that the number of posts he had bought was four less than required. However, he discovered that the number of posts would be just sufficient if he spaced them ten meters apart. What is the length of the side of his property and how many posts did he buy?(1) 160,16 (2) 160,21 (3) 160,17 (4) 180,19

Dist =10(n-1)

Dist =8(n+4-1)

10n-10=8n+24 implies n =17 Length = 160160,17 Choice (3)

QA10305

18.Which one of the following conditions must x, y and z satisfy so that the following system of linear simultaneous equations has at least one solution, such that x + y + z ≠ 0? 3a + 4b - 5c = x, 2a + 7b - 8c = y, 5a - 2b + c = z,(1) 3x - 2y – z = 0 (2) 3x + 2y + z = 0 (3) 3x + 2y – z = 0 (4) 3x -2y + z = 0

(1) Choicez-2y—3x=0c+24b-5a=z16c-14b+4a=2y15c-12b+9a=3x

QA10305

19. In a three digit number, the sum of digits at hundred and tens place is equal to the unit's digit and sum of ten's digit and unit's digit is two and a half times of the hundred's digit. Find the number.(1)437 (2) 214 (3) 639

(4) None of these

c=b+a

c2+b2=a5

c5=b5+c2+b2

c3=b7

25a

=c+b

73

=cb

4 7 3a c b

(1) Choice 437

QA1030520. When the population of two neighboring villages A and B was counted, the following data came up: A has 372 fewer males than B, B has 200 more females than males, A has twice as many males as females, A has 736 fewer females than B, What is the total number of males in A?(1) 329 (2) 841 (3) 328 (4) 364

Males FemalesTown

2x xA

2x+372 2x+572B

2x+572-x=736

x=164

2x=328

A has twice as many males as femalesA has 372 fewer males than B B has 200 more females than malesA has 736 fewer females than B

Chioce (3)

QA1030521. Three people A, B and C have equal amounts of money. A gives half of his money equally to B and C, then B gives half of his amount to C. If C has Rs.3,375, find the total amount with them initially?.(1) Rs. 1,800 (2) Rs. 3,600 (3) RS. 5,450 (4) Rs. 5,400

A B8x 8xInitial4x 10x1st

C8x

10x4x 5x2nd 15x

15x =3375 24x =5400Choice (4)

QA10305

22.A shop stores ‘x’ kgs of rice. The first customer buys half of this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half of the remaining amount and half of a kg of rice. Thereafter no rice is left in the shop. Which of the following best describes the value of x? (CAT 2008)(1)2≤ x ≤ 6 (2) 5 ≤ x ≤ 8 3) 9 ≤ x ≤ 12 (4) 11 ≤ x ≤ 14

C3

2

1

x21

+2x 0=

21

-2x

y21

+2y x=

21

-2y

z21

+2z y=

21

-2z

1=x0=2

1-x⇒

3=y1=2

1-y⇒

7=z3=2

1-z⇒

Chioce (2)

QA1030523. Ramesh went to the market and bought apples, oranges and bananas. He bought a total of 35 fruits. He purchased at least 10 fruits of each variety and calculated that if the cost of each banana was two rupees more and the cost of each orange was three rupees more, then his total expenditure would have gone up by `54. Which of the following could be the total number of apples and oranges he bought? (1) 21 (2) 22 (3) 23 (4) 24

34=b+r+a

exp= bz+ry +ax

54+exp= 2)+b(z+3)+r(y+ax

54= 2b+3rr b

18 016 314 612 910 12

12=a 34=12+10+a ⇒

22=r+a (2) Choice

xxxx

ok

QA10305

then Find (a + b + c)(1) 30 (2) 28 (3) 32(4) None of these

87, = 2c + 5b + 3a 87, = 5c + b + 2a 62, = 3c + 2b + aIf 24.

) 87......(3 = 2c + 5b + 3a) 87......(2 = 5c + b + 2a) 62......(1 = 3c + 2b + a

37 = c+3b 87 = 5c + b + 2a (2)

241= 6c + 4b + a 2 2×) (1 ⇒

99 = c7+b 87 = 2c + b 5 + 3a (3)

186= 9c + 6b + a 3 3×) (1 ⇒

8= b and 13=c29 = c21+3b

37 = c+3b

7=a

28=c+b+a

(2) Choice

QA1030525. A person buys some books at a certain price. The number of books as well as the price is a two-digit number. If the digits of the price are interchanged, then the total cost increases by `477. Find the number of books purchased.(1) 53 (2) 63 (3) 57(4) Cannot be determined

pof digits thereversingby formed

number the is p' where477+x=p'×b

x =p×b

9k=p'-p

1=k and 53=b477=9k×b

477=(p'-p)×b

53=b

(1) Choice

QA10305 Each question is followed by two statements, (I) and (II). Answer each question using the following instructions.(1) If the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.(2) If the question can be answered by using either statement alone.(3) If the question can be answered by using both statements together, but cannot be answered using either statement alone.(4) If the question cannot be answered even by using both statements together.

26. What is the cost of 6 pens and 4 pencils?I. If a person buys 8 pens and 5 pencils, it will cost him `89.II. If a person buys 9 pens and 6 pencils, he will have to pay `24 extra if the price of pen and pencil is increased by 25% and 20% respectively.

1st statement not sufficient

2nd statement not sufficient

Combining8p+5y = 899*1.25p+5*1.2y = 113Sufficient

(3) Choice

QA1030527. Find the value of positive integers x&y.I. 3x + 5y = 24II.7x – 2y = 15.

Each question is followed by two statements, (I) and (II). Answer each question using the following instructions.(1) If the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.(2) If the question can be answered by using either statement alone.(3) If the question can be answered by using both statements together, but cannot be answered using either statement alone.(4) If the question cannot be answered even by using both statements together.

3x + 5y = 24X=3 and y =3Sufficient

7x - 2y = 15x=3 and y =3x=5 and y =10x=7 and y =17insufficient

(1) Choice

QA10305 28. Find the two-digit number.I. Difference between the digits is 2.II. Number is divisible by 6 and when it is increased by 18, the digits get interchanged.



13 3124 4235 5346 6457 7568 8679 97

SecondStatement is sufficient

(1) Choice

QA10305 29. Find the age of the man and his son.I. 6 years hence, father’s age will be twice of son’s age.II. 8 years ago, father’s age was 3 times the age of his son.




f+6 = 2(s+6)f-8 = 3(s-8)14= -S +36S=22F= 50

(3) Choice

QA10305 30. Find the number of questions attempted by Shishir if he attempts all the questions.I. Total marks obtained by Shishir are 45.II. The number of correctly attempted questions is 1 less than twice the number of wrongly attempted questions.




(4) Choice

Marks for right answer andWrong answer not given

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Qa 10305 simple equations