Aptitude::Profit and Loss

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Example 1 / 16

By selling a watch for Rs. 560, a shopkeeper incurs a loss of 20%. Find the cost price of the watch for the shopkeeper.

SP = Rs. 560
Loss% = 20%
Therefore, CP = \(\frac{560}{(100-20)}\) x 100
= \(\frac{560}{80}\) x 100
= Rs. 700 Ans.

CP = \(\frac{SP}{(100-LOSS)}%\)

To get the CP, we have to divide SP by (100-Loss)%.

Example 2 / 16

A cellular phone when sold for Rs. 3808 fetches a profit of 12%. Find the cost price of the cellular phone.

SP = Rs. 3808
Profit% = 12%
CP = \(\frac{3808}{(100+12)}\) x 100
= \(\frac{3808}{(112)}\) x 100
= Rs. 3400 Ans.

CP = \(\frac{SP}{(100+Profit)}\)%

To get the CP, we have to divide SP by (100+Profit)%.

Example 3 / 16

A shopkeeper sells goods for Rs. 1800 and make a profit of 20% in the process. Find his profit percent if he had sold his goods for Rs. 1687.5.

SP = Rs. 1800
Profit% = 20%
CP = \(\frac{1800}{(100+20)}\) x 100
= \(\frac{1800}{(120)}\) x 100
= Rs. 1500 Ans.

CP = \(\frac{SP}{(100-Profit)}%\)

To get the CP, we have to divide SP by (100+Profit)%.

Example 4 / 16

A marble table when sold for Rs. 6400 gives a loss of 11.11% to the merchant who sells it. Calculate his loss or gain percent, if he sells it for Rs. 7812.

SP = Rs. 6400
Loss% = 11.11%
CP = \(\frac{6400}{(100-11.11)}\) x 100
= \(\frac{6400}{(88.89)}\) x 100
= Rs. 7199.91
SP = Rs. 7812
Profit% = \(\frac{Profit}{(CP)}\) x 100
= \(\frac{7812-7199.91}{(7199.91)}\) x 100
= 8.5% Ans.

CP = \(\frac{SP}{(100-LOSS)}%\)
Profit% = \(\frac{Profit}{(CP)}\) x 100

At first, we will take out the CP by the given formula, then, according to the given new SP and CP which has been taken, we will calculate profit%.

Example 5 / 16

A shopkeeper bought 480 chocolates at Rs. 6 per dozen. If he sold all of them at Rs. 0.75 each, what was his profit percent?

Cost of 12 chocolates = Rs. 6
Cost of 1 chocolate = Rs. \(\frac{1}{2}\)
Cost of 480 chocolates = Rs. 240
Now,
Selling price of 1 chocolate = Rs. 0.75
Selling price of 480 chocolates = Rs. 360
Therefore,
CP = Rs. 240
SP = Rs. 360
Therefore, Profit% = \(\frac{360-240}{240}\) x 100
= 50% Ans.

Profit% = \(\frac{(SP-CP)}{CP}\) x 100

At first, take out SP and CP of 480 chocolates, then find profit % by the given formula.

Example 6 / 16

An iron merchant makes a profit of 30% by selling iron at Rs. 26 per quintal. If he sells the iron at Rs. 22.50 per quintal, what is his profit percent on the whole investment?

Profit% = 30%
SP = Rs. 26
CP = \(\frac{26}{100+30}\) x 100
= Rs. 20
Now,
SP = 22.50
Profit% = \(\frac{2.5}{20}\) x 100
= 12.5% Ans.

CP = \(\frac{SP}{(100+Profit)}%\)

At first, take out the CP and find Profit% with the given SP and CP.

Example 7 / 16

A pet shop owner sells two puppies at the same price. On one he makes a profit of 25% and on the other, he suffers a loss of 25%. Find his loss or gain percent on the whole transaction.

Here, the SP is same.
CP Profit/Loss SP
100 +25 125 --- x 3
100 -25 75 --- x 5
300 +75 375
500 -125 375
------ ---------
800 -50
Hence, Loss% = \(\frac{50}{100}\) x 100
= 6.25% Ans.

Loss% = \(\frac{Loss}{100}\) x 100

The question has been solved by a very simple shortcut. It is given that the SP is the same. So, we will do the calculation and make the SP same. Some steps are given to solve this:
1.Consider the CP of both to be Rs. 100.
2.Now, add Profit to one CP and subtract the loss from another CP. After, doing this we will get SP of both.
3. Now, in order to make both the SP same, multiply whole CP and profit/loss, with a suitable number.
4. Now, the SP will become the same and accordingly, profit% or loss% will be obtained.
5. Hence, we get the answer.

Example 8 / 16

125 toffees cost Rs. 75. Find the cost of one million toffees if there is a discount of 40% on the selling price for this quantity.

Cost of 125 toffees = Rs. 75
Cost of 1 toffee = Rs. \(\frac{75}b {125}\)
Therefore, cost of 1,000,000 toffees = \(\frac{75}{125}\) x 1000000
= Rs. 6,00,000
Now, after allowing 40% discount,
cost = 600000 - \(\frac{40}{100}\) x 600000
= Rs. 3,60,000 Ans.

Cost = CP- Discount% of CP

At first, find the cost of 1 million toffees, then subtract the discount from it.

Example 9 / 16

A dozen pairs of gloves quoted at Rs. 120 are available at a discount of 20%. Find how many pairs of gloves can be bought for Rs. 16.

MP = Rs. 120
discount% = 20%
SP = 120 - \(\frac{20}{100}\) x 120
= Rs. 96
Hence, SP of 12 gloves = Rs. 96
So, SP of 1 glove = Rs. 8
Now,
No. of gloves that can be bought at Rs. 8 = 1
Therefore, no. of gloves that can be bought at Rs. 16 = 2 gloves Ans.

SP = MP – MP*Discount%

At first find the SP according to the given formula, then by applying unitary method, find No. of gloves.

Example 10 / 16

Find a single discount, equivalent to the discount series of 25%, 20%, 10%.

Let the MP = Rs. 100
After allowing a discount of 25% on Rs. 100,
SP = 100 - \(\frac{25}{100}\) x 100 = Rs. 75
After allowing a discount of 20% on Rs. 75,
SP = 75 - \(\frac{20}{100}\) x 75 = Rs. 60
After allowing a discount of 10% on Rs. 60,
SP = 60 - \(\frac{10}{100}\) x 60 = Rs. 54
Therefore, the equivalent discount = 100 – 54 = 46% Ans.

SP = MP-MP*Discount%.

At first, take, the MP to be 100. Then according to the formula, make the discount for consecutive three times, and subtract the result by 100 to get the equivalent discount.

Example 11 / 16

How much more than the cost price should a shopkeeper mark his goods, so that after allowing a discount of 6.25% he should have a gain of 25% on his outlay?

Let the CP = Rs. 100
Now, SP = 100 + \(\frac{25}{100}\) x 100
= Rs. 125
We know,
SP = MP - \(\frac{discount}{100}\) x MP
or, 125 = MP - \(\frac{6.25}{100}\) x MP
or, MP = Rs. 133.33
Therefore, the shopkeeper must mark his goods 33.33% more than the CP. Ans.

SP = CP+CP*Profit%
SP = MP – Discount% x MP

Take out the SP accordingly of the two and compare how much MP with CP.

Example 12 / 16

A whole-seller allows a discount of 25% on the list price to the retailer. The retailer sells at 10% discount on the list price. If the customer paid Rs. 54 for an article, what is the profit by the retailer?

Let MP be Rs. X
For the whole-seller,
SP = X - \(\frac{25}{100}\) x X
= Rs. \(\frac{3x}{4}\)
For the retailer,
CP = Rs. \(\frac{3x}{4}\)
SP = X - \(\frac{10}{100}\) x X
= Rs. \(\frac{9x}{10}\)
Now,
54 = \(\frac{9x}{10}\)
Therefore, X = Rs. 60
So, CP = Rs. 45
Hence, profit = 54 – 45 = Rs. 9 Ans.

SP = MP – MP*Discount%
Profit= SP-CP

At first, find the SP for the whole-seller, then, the SP of the whole-seller becomes CP of the retailer. Now, find SP, MP and CP according to the question and then, find the profit.

Example 13 / 16

A man sells 5 articles for Rs. 15 and makes a profit of 20%. Find his gain or loss percent if he sells 8 articles for Rs. 18.40.

SP of 5 articles = Rs. 15
SP of 1 article = Rs. 3
Profit% = 20%
Therefore, CP = \(\frac{3}{120}\) x 100
= Rs. \(\frac{10}{4}\)
Now, SP of 8 articles = Rs. 18.40
SP of 1 article = Rs. \(\frac{23}{10}\)
Hence, loss = \(\frac{10}{4}\) - \(\frac{23}{10}\)
= Rs. \(\frac{8}{40}\)
And, loss% = \(\frac{8}{40}\) x \(\frac{4}{10}\) x 100
= 8% Ans.

CP = \(\frac{SP}{(100+Profit)}%\)
Loss= CP-SP
Loss%= \(\frac{LOSS}{CP}\)*100

At first, find SP and CP of 1 article and find the loss%. Simply based on direct formula.

Example 14 / 16

Vikas bought an article at Rs. 150 and sold it at a profit of 20%. What would have been the increase in the profit percent if it was sold for Rs. 195?

CP = Rs. 150
profit% = 20%
Now, SP = 150 x \(\frac{120}{100}\) = Rs. 180
New SP = Rs. 195
Now, profit% = \(\frac{195-150}{150}\) x 100 = 30%
Hence, increase in profit% = 10% Ans.

SP = CP x (100+Profit)%
profit% = \(\frac{SP-CP}{CP}\) x 100

Initial profit is given, now, with the help of new SP given, find the new profit %, the difference between the two profit % will give the increase in profit %.

Example 15 / 16

If the cost price of 25 articles is equal to the selling price of 15 articles, find the profit percent.

Given:
CP of 25 articles = SP of 15 articles
Let, CP of 1 article = Re. 1
So, CP of 15 articles = Rs. 15
SP of 15 articles = Rs. 25
Therefore, profit% = \(\frac{25-15}{15}\) x100
= \(\frac{10}{15}\) x 100
= 66.67% Ans.

profit% = \(\frac{SP-CP}{CP}\) x100

In this type of problem change either one SP/CP according to the number of articles and keep the other CP/SP same. Both numbers of articles must be same, then calculate profit %.

Example 16 / 16

A dealer buys eggs at Rs. 72 per gross. He sells the eggs at a profit of 6.25% on the cost price. What is the selling price per egg (approximately)?

A gross means 144 eggs.
Thus, the cost price per egg =\(\frac{144}{72}\)
= 50 paise
Now,
selling price after a 6.25% profit =
SP = 50 + \(\frac{6.25}{100}\) x 50
53 paise (approx.).Ans.

SP CP + CP* (Profit%)

Based on the formula directly.

Aptitude::Profit and Loss

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