# Aptitude::Profit and Loss

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Example 1 / 16

SP = Rs. 560

Loss% = 20%

Therefore, CP = \(\frac{560}{(100-20)}\) x 100

= \(\frac{560}{80}\) x 100

= Rs. 700

Loss% = 20%

Therefore, CP = \(\frac{560}{(100-20)}\) x 100

= \(\frac{560}{80}\) x 100

= Rs. 700

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

NA

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

Example 2 / 16

SP = Rs. 3808

Profit% = 12%

CP = \(\frac{3808}{(100+12)}\) x 100

= \(\frac{3808}{(112)}\) x 100

= Rs. 3400

Profit% = 12%

CP = \(\frac{3808}{(100+12)}\) x 100

= \(\frac{3808}{(112)}\) x 100

= Rs. 3400

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

NA

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

Example 3 / 16

SP = Rs. 1800

Profit% = 20%

CP = \(\frac{1800}{(100+20)}\) x 100

= \(\frac{1800}{(120)}\) x 100

= Rs. 1500

Profit% = 20%

CP = \(\frac{1800}{(100+20)}\) x 100

= \(\frac{1800}{(120)}\) x 100

= Rs. 1500

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

NA

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

Example 4 / 16

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%

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

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

NA

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

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%

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

NA

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

Example 6 / 16

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%

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

NA

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

Example 7 / 16

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%

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

NA

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.

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

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

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

NA

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

Example 9 / 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

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%

NA

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

Example 10 / 16

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%

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%.

NA

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

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.

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

SP = MP – Discount% x MP

NA

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

Example 12 / 16

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

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

Profit= SP-CP

NA

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

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%

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

Loss= CP-SP

Loss%= \(\frac{LOSS}{CP}\)*100

NA

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

Example 14 / 16

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%

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

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

NA

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

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%

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

NA

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 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.).

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%)

NA

Based on the formula directly.