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Aptitude

Solving Profit & Loss Quickly

Profit and Loss is the most important topic in quantitative section of all the job entrance exams. This page here on contains information about how to solve Profit and Loss questions.

Gain or Profit – If Cost Price is lesser than Selling Price, gain is made.

Loss – If Cost price is greater than the Selling price, Loss is incurred

Basic Concepts:

Concepts to solve Profit and loss questions:

  • Cost Price – It is basically the price at which a commodity or object is bought at. e.g. Shopkeeper buying Sugar from Farmer to sell in his grocery store. In its short form it is denoted as C.P.
  • Selling Price – The price at which the commodity is sold at. e.g. Shopkeeper selling sugar to his customer. In its short form is denoted as S.P.
  • Gain or Profit – If Cost Price is lesser than Selling Price, gain is made.
  • Loss – If Cost price is greater than the Selling price, Loss is incurred.
How to Solve Profit and Loss Questions Quickly

1. A man sold two chairs at Rs. 1200 each. On one he gained 20% and on the other he loss 20%. His gain or loss in the whole transaction is:

Options:

A. 1% loss

B. 2% loss

C. 4% loss

D. 15% gain

Solution:

In the case where loss and gain percentage is common on same selling price, always a loss incurs in total deal. And this can be calculated by a short-cut:

Loss on total deal,

$\eqalign{ & = {\left( {\frac{{{\text{Common loss or gain percentage}}}}{{10}}} \right)^2} \cr & = {\left( {\frac{{20}}{{10}}} \right)^2} \cr & = 4\% \cr} $

Alternatively, It can be also calculated through Graphic Change Method: This can be given by,
100 == 20% gain ⇒ 120 == 20% loss ⇒ 96
Loss = 4% (As 100 became 96)

Correct option: C

2. If on an item a Shop Keeper gives 25% discount and earn 25% profit. If he now give 10% discount then what is the profit percentage.

Options:

A. 40%

B. 55%

C. 35%

D. 30%

Solution:

Let the cost be Rs x.

After giving 25% discount it becomes 0.75x

Selling price = 0.75x which gives 25% profit… (1)

Thus, after giving 10% discount it becomes 0.90x

Selling price = 0.90x …… (2)

From (1) and (2),

0.90x will gives$ \frac{25 × 0.90x}{0.75x} = 30 %$ profit.

Correct option: D

3. A dealer buys an article marked at Rs. 25,000 with 20% and 5% off. He spends Rs. 1,000 for its repairs and sells it for Rs. 25,000. What is his gain or loss per cent?

Options:

A. 25% loss

B. 25% gain

C. 10% gain

D. 10% loss

Solution:

Marked Price = 25000.
After first discount it become,
= 25000 - 20% of 25000 = 20000.
After second discount, it becomes
= 20000 - 5% of 20000 = 19000.
So, SP = 19000.
CP for the man who bought it, as he spends 1000 on repair.
= 19000 + 1000 = 20000
Profit = 25000 - 20000 = 5000.
%Profit = \frac{5000 \times 100}{20000} = 25%

25000(MP) == 20%(Disc.) ⇒ 20000 == 5%(disc.) ⇒19000(CP)
Spends on repair = Rs. 1000
Then, CP becomes = 19000 + 1000 = 20000
Profit = 5000
%Profit = \frac{5000 \times 100}{20000} = 25%

Correct Option: B

How To Solve Questions based on Given Percentage

1.A shopkeeper bought a watch for Rs.200 and sold it for Rs.400.What is his profit percentage?

Options:

A. 100%

B. 125%

C. 90%

D. 50%

Solution:

Selling price = 400

profit % =$\frac{Total \: Profit}{Cost\: Price}$

profit=400-200=rs.200

profit % = $\frac{200}{200}$

∴ S.P = 1.0 x

$ = \frac{100}{1}$

= 100%

Correct option: A

2.A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.55 more he would have had a profit of 40%. The cost price of the article is.

Options:

A. 125

B. 250

C. 112.5

D. 250.5

Solution:

Now x is CP , sold it at a loss of 10% = $\frac{90x}{100} =\frac{9x}{10}$

Bought it for 20% less = $\frac{80x}{100} = \frac{4x}{5}$

profit 40% of $ \frac{4x}{5} = \frac{140}{100} ×\frac{4x}{5}=\frac{56x}{50}$

$\frac{56x}{50}–\frac{9x}{10} = 55rs$

$\frac{560x-450x}{500} = 55rs$

$\frac{110x}{500} = 55rs$

$x=\frac{500*55}{110}$

$x=\frac{27500}{110}$

X-250

Correct option: B

3.If on an item a company gives 25% discount, they earn 25% profit. If they now give 10% discount then what is the profit percentage.

Options:

A. 40%

B. 55%

C. 45%

D. 30%

Solution:

Let the cost be Rs x.

After giving 25% discount it becomes 0.75x

Selling price = 0.75x which gives 25% profit…(1)

Thus, after giving 10% discount it becomes 0.90x

Selling price = 0.90x ……(ii)

From (1) and (2),

0.90x will gives = $\frac{25 * 0.90x}{0.75x}$

= 30 % profit.

Correct Option: D

4. A cow and a horse are bought for Rs 200000. The cow is sold at profit of 20% and the horse at a loss of 10%. The overall gain is Rs 5000. The cost price of cow is?

Options:

A. 36000

B. 80000

C. 60000

D. 45000

Solution:

Given that a cow and a horse bought at 200000. Cow sold at profit 20% and horse at loss 10%. Overall gain is 4000.

We are to find the cost price of cow.

Let x and y represents the cost price of cow and horse respectively.

Then, according to the given information, we have

$ x + y = 200000 $

$ y = 200000 - x $ [equation - i]

$20 \% \times x -10% \times y = 4000 $

$ \frac{20}{100} \times x - \frac{10}{100} \times y = 4000$

$\frac{x}{5} - \frac{y}{10} = 4000$

$2x - y = 40000$

$2x - (200000 - x) = 40000$ [using equation i]

$2x - 200000 + x = 40000$

$3x = 240000$

$x = \frac{240000}{3}$

$x = 80000$

Correct option: B

5. A merchant buys 200 kg of rice at Rs. 1.25 per kg, 400 kg of wheat at 75 paise per kg and 300 kg of Jwar at 50 paise per kg. He sells 100 kg of rice at a loss of 25%. 100 kg of wheat at a profit of 25% and 100 kg of Jawar at a profit of 30%. He then mixes the rest and sells $\frac{1}{3}$ of the mixture at 1 rupee per kg. At what rate he should sell the remaining mixture so that he earn a profit of 25% on the whole outlay?

Options:

A. Rs 1

B. Rs 1.12

C. Rs 1.06

D. Rs 1.15

Solution:

Total CP of Rice =200×1.25= Rs. 250

Total CP of Wheat =400 × 0.75 = Rs. 300

Total CP of Jawar =300 × 0.5 = Rs. 150

Total cost = 250 + 300 + 150 = Rs. 700

CP + 25% profit = 700 + 25% of 700 = Rs. 875

He sells 100 kg rice at 25% loss.

SP of 100 kg rice $ = 125 − 25% of 125 = 125 − \frac{25}{100} \times 125 = 93.75 $

SP of 100 kg wheat $ = 75 + 25% of 75 = 75 + \frac{25}{100} \times 75 = 93.75 $

SP of 100 kg Jawar = 50 + 30% of 50 = 50 + \frac{30}{100} \times 50 = 65 $

Now, he mixes, 100 kg rice, 300 kg wheat and 200 kg jawar , Total mixture = 100 + 300 + 200 = 600kg

He sells $\frac{1}{3} $ mixture i.e. 200 kg of mixture at price 1 rupee per kg. So, SP = 200

Remaining Mixture = 400 kg

Till now SP = 93.75 + 93.75 + 65 + 200 = Rs. 452.5

Now, he needs, 875 − 452.5 = Rs.422.5 to get 25% profit.

So, selling price of remaining mixture $ = \frac{422.5}{400} = Rs. 1.06 $

Correct Option: C