Quantitative Aptitude Profit, Loss and Discount Formulas E ...

Quantitative Aptitude – Profit, Loss and Discount – Formulas E-book


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Quantitative Aptitude – Profit, Loss and Discount– 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 – 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. – C.P.

⇒ S.P. = C.P. + Profit

⇒ C.P. = S.P. – 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.


Solution: Given: cost price = Rs. 15, selling price = Rs. 40

Profit = selling price – cost price = Rs. 40 – 15 = Rs. 25

The profit as a percentage of the cost price:

Profit % = 𝑃𝑟𝑜𝑓𝑖𝑡

𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 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. – S.P.

C.P. = S.P. + Loss

S.P. = C.P. – 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 ∴Loss = Cost price – selling price = Rs. (150 – 137.50) = Rs. 12.50 Now, Percentage

Loss

=𝐿𝑜𝑠𝑠 x 100

𝐶𝑜𝑠𝑡 𝑃𝑟𝑖𝑐𝑒%

= 12.50 x 100

150%= 8.33%

FORMULA 2:

When cost price and percentage profit are given, then selling price = Cost Price [ 𝟏𝟎𝟎+𝑷𝒓𝒐𝒇𝒊𝒕%

𝟏𝟎𝟎]

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


FORMULA 3:

When cost price and percentage loss are given, then Selling price = cost price =[𝟏𝟎𝟎−𝑳𝒐𝒔𝒔

𝟏𝟎𝟎]

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 =[100−𝐿𝑜𝑠𝑠

100]

= Rs. 420[100−15

100] = [

420 x 85

100]

= Rs. 357

FORMULA 4:

When selling price and percentage profit are given, then

Cost price = selling price[𝟏𝟎𝟎

𝟏𝟎𝟎+𝒑𝒓𝒐𝒇𝒊𝒕%]

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%

∴ Cost price = selling price[100

100+𝑝𝑟𝑜𝑓𝑖𝑡%]

= 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[𝟏𝟎𝟎

𝟏𝟎𝟎 − 𝑳𝒐𝒔𝒔]

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 − 𝐿𝑜𝑠𝑠]


= Rs. 376 × [100

100 − 6]

= Rs. 376 × [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 by𝒙𝟐

𝟏𝟎𝟎 % and the value of loss is given by

𝟐𝒙𝟐𝑹

(𝟏𝟎𝟎𝟐− 𝒙𝟐)

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 [𝒙𝟐

𝟏𝟎𝟎] % =[

10 ×10

100 ] % = 1%

FORMULA 6:

A dishonest shopkeeper claims to sell goods at cost price, but uses a lighter weight, then his Gain % =

[𝟏𝟎𝟎×𝐞𝐱𝐜𝐞𝐬𝐬

𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍 𝒗𝒂𝒍𝒖𝒆−𝒆𝒙𝒄𝒆𝒔𝒔]

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 % = [100×excess

𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑣𝑎𝑙𝑢𝑒−𝑒𝑥𝑐𝑒𝑠𝑠]

= [10

8]= [

100×excess

1−𝑒𝑥𝑐𝑒𝑠𝑠]

From here, Excess = 0.111... Kg, which is 111.11 grams Weight used by shopkeeper = 1000 – 111.11 = 888.89

grams

Example 9:


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. = 𝑅𝑠. [(20+8)×200

8]

= Rs. 28 × 25 = Rs. 700.

FORMULA 7:

If cost price of x articles is equal to the selling price of y articles, then profit/loss percentage

=[𝒙−𝒚

𝒚]x 100%

According to +ve or –ve 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 % =[−5

20] x 100

= –25% loss, since it is –ve.

FORMULA 8:

The reduction made on the ‘marked price’ of an article is called the discount. When no discount is

given, ‘selling price’ is the same as ‘marked price’. Discount = Marked price × Rate of discount. S.P. =

M.P. – Discount. Discount % = =[𝑫𝒊𝒔𝒄𝒐𝒖𝒏𝒕

𝑴.𝑷.] 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

∴ M.P. should be Rs. 133 1

3

FORMULA 9:


Buy x get y free i.e., if x + y articles are sold at cost price of x articles, then the percentage discount

= 𝒚

𝒙+𝒚 x 100

Example 12:

Find the single discount equivalent to successive discounts of 15% and 20%.

Solution: By direct formula,

Single discount

[a + b - 𝑎𝑏

100]%

[15 + 20 –15 x 20

𝑥+𝑦]%

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 d₁ and d₂ are given successively on it then, Final price =

list price [1 – 𝑑1

100] [1 –

𝑑2

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 – 6.5 = Rs. 58.5

Therefore, the second discount

= [58.5−56.15

58.5] x 100 = 4%


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 – C.P

If C.P>S.P, then Loss, L = C.P – S.P

% Profit or Gain percentage or Profit Percentage = Profit/CP × 100

%Loss = Loss/CP × 100

Discount = M.P – S.P (If no discount is given, then M.P = S.P)

%Discount = Discount/MP × 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 𝒙𝟐

𝟏𝟎𝟎% The absolute value of loss =

𝟐𝒙𝟐𝑹

(𝟏𝟎𝟎𝟐− 𝒙𝟐)

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 – Error) x100%

Tip 5

S.P = (([100

100+𝑝𝑟𝑜𝑓𝑖𝑡%]) C.P ( If S.P > C.P )

S.P=(([100

100−𝐿𝑜𝑠𝑠%]) C.P (If S.P < C.P ) [

100 × S.P

100+𝑝𝑟𝑜𝑓𝑖𝑡%]

C.P= ([100 × S.P

100+𝑝𝑟𝑜𝑓𝑖𝑡%]) (If S.P >C.P )


C.P= ([100 × S.P

100−𝐿𝑜𝑠𝑠%] (If S.P <C.P )

Tip 6

Buy x get y free, then the %discount = [𝑦

𝑥+𝑦] 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 – [𝑎∗𝑏

100])

If C.P of x article is equal to the selling price of y articles then the, Resultant profit % or loss % = [ 𝑦−𝑥

𝑦] ×

100

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