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Quantitative Aptitude β Profit, Loss and Discount β Formulas E-book
Quantitative Aptitude β Profit, Loss and Discount β Formulas E-book
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Quantitative Aptitude β Profit, Loss and Discount β Formulas E-book
Quantitative Aptitude β Profit, Loss and Discountβ Formulas
Introduction to Quantitative Aptitude:
Quantitative Aptitude is an important section in the employment-related competitive exams in India.
Quantitative Aptitude Section is one of the key sections in recruitment exams in India including but not
limited to Banking, Railways, and Staff Selection Commission, Insurance, Teaching, UPSC and many
others. The Quantitative Aptitude section has questions related to Profit and Loss, Percentage and
Discount, Simple Equations, Time and Work and Quadratic Equations etc.
Profit, Loss and Discount β Important Terms:
1. What is Profit?
When selling price is greater than the cost price then the seller is said to have profit. Profit is
also known as gain.
2. What is Loss?
When selling price is less than the cost price then the seller is said to have loss.
3. What is Selling Price (S. P.)?
The price, at which a store sells the goods, is called its selling price.
4. What is Cost Price (C. P.)?
The price, at which a store owner purchases goods, is called its cost price.
Note:
Thus, If S.P. > C.P., then
Profit = S.P. β C.P.
β S.P. = C.P. + Profit
β C.P. = S.P. β Profit
Profit, Loss and Discount- Aptitude Test Tricks & Shortcuts & Formulas& Examples
Example 1:
A shopkeeper buys scientific calculators in bulk for Rs. 15 each. He sells them for Rs. 40 each.
Calculate the profit on each calculator in rupees, and as a percentage of the cost price.
Quantitative Aptitude β Profit, Loss and Discount β Formulas E-book
Solution: Given: cost price = Rs. 15, selling price = Rs. 40
Profit = selling price β cost price = Rs. 40 β 15 = Rs. 25
The profit as a percentage of the cost price:
Profit % = ππππππ‘
πππππππ‘πππ x 100%
25 x 100
15% = 166.7%
FORMULA 1:
If the selling price (S.P.) of an article is less than the cost price (C.P.), then the difference between the
cost price (C.P.) and the selling price (S.P.) is called loss. Thus, if S.P. < C.P., then
Loss = C.P. β S.P.
C.P. = S.P. + Loss
S.P. = C.P. β Loss
Example 2:
If the cost price of a book is Rs. 150 and selling price is 137.50, then calculate the loss and percentage loss on
the book?
Solution: Here, cost price = Rs. 150
And selling price = Rs. 137.50 β΄Loss = Cost price β selling price = Rs. (150 β 137.50) = Rs. 12.50 Now, Percentage
Loss
=πΏππ π x 100
πΆππ π‘ πππππ%
= 12.50 x 100
150%= 8.33%
FORMULA 2:
When cost price and percentage profit are given, then selling price = Cost Price [ πππ+π·πππππ%
πππ]
Example 3:
A chair was purchased for Rs. 470 and sold at a profit of 10%. Find the selling price.
Solution: Here, cost price = Rs. 150
= 470 [100+10
100] = 470 x
470
100 = Rs. 517
Quantitative Aptitude β Profit, Loss and Discount β Formulas E-book
FORMULA 3:
When cost price and percentage loss are given, then Selling price = cost price =[πππβπ³πππ
πππ]
Example 4:
A person bought a table for Rs. 420 and sold at the loss of 15%. Find the selling price of table?
Solution: Selling price = cost price =[100βπΏππ π
100]
= Rs. 420[100β15
100] = [
420 x 85
100]
= Rs. 357
FORMULA 4:
When selling price and percentage profit are given, then
Cost price = selling price[πππ
πππ+ππππππ%]
Example 5:
A Chair was sold for Rs. 517 at a profit of 10%. Find the cost price of the chair
Solution: Here, selling price = Rs. 517 and profit = 10%
β΄ Cost price = selling price[100
100+ππππππ‘%]
= 517[100
100+10]
= 517 x[100
110] = Rs. 470
FORMULA 5:
When selling price and percentage loss are given, then Cost price = Selling price[πππ
πππ β π³πππ]
Example 6:
Ram sold a watch for Rs. 376 at a loss of 6%. Find the cost price of the watch.
Solution: Cost price = Selling price[100
100 β πΏππ π ]
Quantitative Aptitude β Profit, Loss and Discount β Formulas E-book
= Rs. 376 Γ [100
100 β 6]
= Rs. 376 Γ [100
94]
FORMULA 5:
If two items are sold each at rupees R, one at a gain of x% and other at a loss of x %, there is always an
overall loss given byππ
πππ % and the value of loss is given by
ππππΉ
(ππππβ ππ)
In case the cost price of both the items is the same and percentage loss and gain are equal, then net
loss or profit is zero. The difference between the two cases is that the cost price in the first case is not
the same, and in the second case it is the same.
Example 7:
Ram sells two Mobile phones for Rs. 1000 each, one at a profit of 10% and other at a loss of 10%. Find his gain
or loss percentage.
Solution: Using the formula,
Loss [ππ
πππ] % =[
10 Γ10
100 ] % = 1%
FORMULA 6:
A dishonest shopkeeper claims to sell goods at cost price, but uses a lighter weight, then his Gain % =
[πππΓππ±πππ¬π¬
ππππππππ πππππβππππππ]
Example 8:
A shopkeeper sells rice to a customer, using false weights and gains 100/8 % on his cost. What weight has he
substituted for a kilogram?
Solution: Using the formula,
Gain % = [100Γexcess
ππππππππ π£πππ’πβππ₯πππ π ]
= [10
8]= [
100Γexcess
1βππ₯πππ π ]
From here, Excess = 0.111... Kg, which is 111.11 grams Weight used by shopkeeper = 1000 β 111.11 = 888.89
grams
Example 9:
Quantitative Aptitude β Profit, Loss and Discount β Formulas E-book
A table is sold at a profit of 20%. If the cost price and selling price are Rs. 200 less, the profit would be 8% more.
Find the cost price.
Solution: By direct method,
C.P. = π π . [(20+8)Γ200
8]
= Rs. 28 Γ 25 = Rs. 700.
FORMULA 7:
If cost price of x articles is equal to the selling price of y articles, then profit/loss percentage
=[πβπ
π]x 100%
According to +ve or βve sign respectively.
Example 10:
If the C.P. of 15 tables be equal to the S.P. of 20 tables, find the loss per cent.
Solution:By direct method,
Profit/Loss % =[β5
20] x 100
= β25% loss, since it is βve.
FORMULA 8:
The reduction made on the βmarked priceβ of an article is called the discount. When no discount is
given, βselling priceβ is the same as βmarked priceβ. Discount = Marked price Γ Rate of discount. S.P. =
M.P. β Discount. Discount % = =[π«πππππππ
π΄.π·.] X 100
Example 11:
How much % must be added to the cost price of goods so that a profit of 20% must be made after throwing off
a discount of 10% from the marked price?
Solution: Let C.P. = Rs. 100, then S.P. = Rs. 120
Also, Let marked price be Rs. x. Then, 90% of x = 120
X = 120 x 100
90 = 133
1
3
β΄ M.P. should be Rs. 133 1
3
FORMULA 9:
Quantitative Aptitude β Profit, Loss and Discount β Formulas E-book
Buy x get y free i.e., if x + y articles are sold at cost price of x articles, then the percentage discount
= π
π+π x 100
Example 12:
Find the single discount equivalent to successive discounts of 15% and 20%.
Solution: By direct formula,
Single discount
[a + b - ππ
100]%
[15 + 20 β15 x 20
π₯+π¦]%
Successive Discounts
In successive discounts, first discount is subtracted from the marked price to get net price after the first
discount. Taking this price as the new marked price, the second discount is calculated, and it is subtracted
from it to get net price after the second discount. Continuing in this manner, we finally obtain the net
selling price. In case of successive discounts, a% and b%, the effective discount.
If the list price of an item is given and discounts dβ and dβ are given successively on it then, Final price =
list price [1 β π1
100] [1 β
π2
100]
Example 13:
An article is listed at Rs. 65. A customer bought this article for Rs. 56.16 and got two successive discounts of
which the first one is 10%. The other rate of discount of this scheme that was allowed by the shopkeeper was:
1. 3%
2. 4%
3. 6%
4. 2%
Solution:
Price of the article after first discount = 65 β 6.5 = Rs. 58.5
Therefore, the second discount
= [58.5β56.15
58.5] x 100 = 4%
Quantitative Aptitude β Profit, Loss and Discount β Formulas E-book
Quick Reads:
Tip 1
Cost Price
The amount paid to purchase an article or the cost of manufacturing an article is called Cost Price (C.P)
Selling Price
The price at which a product is sold is called Selling price (S.P)
Marked Price
The price at which an article is marked is called Marked price (M.P)
Tip 2
If S.P>C.P, then Profit or Gain, P = S.P β C.P
If C.P>S.P, then Loss, L = C.P β S.P
% Profit or Gain percentage or Profit Percentage = Profit/CP Γ 100
%Loss = Loss/CP Γ 100
Discount = M.P β S.P (If no discount is given, then M.P = S.P)
%Discount = Discount/MP Γ 100
Tip 3
Total increase in price due to two subsequent increases of X% and Y% is X+Y+ XY
100%
If two items are sold at same price, each at Rs. x, one at a profit of P% and other at a loss of x% then there
will be overall loss of ππ
πππ% The absolute value of loss =
ππππΉ
(ππππβ ππ)
Tip 4
If C.P of two items is same, and by selling of each item he earned p% profit on one article and p% loss on
another, then the there will be no loss or gain.
If a trader professes to sell at C.P but uses false weight, then
Gain% = Error
(True Value β Error) x100%
Tip 5
S.P = (([100
100+ππππππ‘%]) C.P ( If S.P > C.P )
S.P=(([100
100βπΏππ π %]) C.P (If S.P < C.P ) [
100 Γ S.P
100+ππππππ‘%]
C.P= ([100 Γ S.P
100+ππππππ‘%]) (If S.P >C.P )
Quantitative Aptitude β Profit, Loss and Discount β Formulas E-book
C.P= ([100 Γ S.P
100βπΏππ π %] (If S.P <C.P )
Tip 6
Buy x get y free, then the %discount = [π¦
π₯+π¦] x 100
(here x+y articles are sold at C.P of x articles.)
When there are two successive discounts of a% and b% are given then the,
Resultant discount = (a + b β [πβπ
100])
If C.P of x article is equal to the selling price of y articles then the, Resultant profit % or loss % = [ π¦βπ₯
π¦] Γ
100
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