CMAT Profit and Loss Questions

Statement I:

It is given, profit percentage = 20%

This implies, $$SP=\frac{120}{100}CP$$

It is given, $$\frac{120}{100}CP-CP=240$$

$$\frac{20}{100}CP=240$$

$$CP=1200$$

SP = 1200+240 = Rs 1440

Therefore, statement I is correct.

Statement II:

It is given,

10CP = 7SP

Profit % = $$\ \frac{\ SP-CP}{CP}\times100=\frac{300}{7}=42\frac{6}{7}\%$$

Therefore, statement II is correct.

The answer is option A.

It is given,

320SP = 400CP

4SP = 5CP

Profit percentage = $$\ \frac{\ SP-CP}{CP}\times100=\ \frac{\ \frac{5CP}{4}-CP}{CP}\times100=25\%$$

The answer is option D.

A : B : C : D = 24($$\frac{3}{12}$$) : 10($$\frac{5}{12}$$) : 35($$\frac{4}{12}$$) : 21($$\frac{3}{12}$$)

A : B : C ; D = 6 : $$\frac{25}{6}$$ : $$\frac{35}{3}$$ : $$\frac{21}{4}$$

A : B: C : D = 72 : 50 : 140 : 63

Anil's rent = $$\frac{72}{72+50+140+63}\times\ $$ Total rent

720 = $$\frac{72}{325}\times\ $$ T

T = Rs 3,250

Answer is option B.

Given, cost price is 80% of selling price

C.P = 0.8 S.P

Profit = $$\ \frac{\ S.P\ -\ C.P}{C.P}\times\ 100$$

         = $$\ \frac{\ S.P\ -\ 0.8S.P}{0.8S.P}\times\ 100$$

         =$$\ \frac{0.2}{0.8}\times\ 100$$

         = 25%

Answer is option B

Profit share = Investment * Time period 
Now we get ratio of profit of A and B :
$$\frac{50,000\times\ 3\ +\ 40,000\times\ 9}{60,000\times\ 3\ +\ 80,000\times\ 6}$$
we get ratio as $$\frac{510}{660\ }=\ \frac{17}{22}$$

It is given that Mohan bought a trouser at 10% discount and sold it to Sohan at a loss of 10%
Now Sohan paid Rs 729
So S.P for Mohan = 729 
This is sold at 10% loss 
so cost price of Mohan = 729/0.9 =810
Now Mohan bought for 810 at 10% discount
so original price (1-0.1) =810
We get undiscounted  price = 900

Let cost price be 1000 per Kg of rice 
Now to make 25% profit at 1000
He will sell 800 gm of rice
Now C.P of 800 gm of rice = 800
Now he sold at 10% less than 1000 so S.P = 900
Now therefore profit = $$\frac{900-800}{800}\times\ 100\ =\ \frac{100}{8}=12.5\ \%$$

Production of unit B in April = 180
Production of unit B in June = 160
Now therefore percentage decrease = $$\frac{\left(180-160\right)}{180}\times\ 100\ \approx\ \ 11\%$$

Two successive discounts of $$x$$ and $$y$$ $$\equiv x+y-\frac{xy}{100}$$

= $$12+8-\frac{12\times8}{100}$$

= $$20-0.96=19.04\%$$

=> Ans - (B)

Let cost price of each article = Rs. 100 and number of articles sold be $$x$$

=> Original selling price price = Rs. 125

=> Original profit = Rs. $$(125-100)x = Rs.$$ $$25x$$

After offering discount of 8%, => New selling price = $$\frac{92}{100}\times125=Rs.$$ $$115$$

Also, new cost price = $$\frac{95}{100}\times100=Rs.$$ $$95$$

$$\because$$ Sale increases by 25%, => Number of articles now sold = $$1.25x$$

=> New profit = Rs. $$(115-95)\times1.25x = Rs.$$ $$25x$$

$$\therefore$$ There is no change in profit.

=> Ans - (A)

If 64 mangoes are sold at Rs.2000, each mango will be sold at Rs. $$\frac{2000}{64}$$

Hence Selling price (S.P) of each mango = Rs. 31.25

Given loss percentage of vendor at this S.P = 40%

Loss percentage = $$\frac{C.P - S.P}{C.P}\times 100$$ 

$$\Rightarrow \frac{40}{100} = \frac{C.P - S.P}{C.P}$$

$$\Rightarrow S.P = 0.6\times C.P$$

$$\Rightarrow C.P = \frac{31.25}{0.6} = 52$$

Therefore Cost Price of 1 mango (C.P) = Rs. 52

Let us calculate the S.P of each mango in order to get a 20% gain.

Gain percentage = $$\frac{S.P - C.P}{C.P}\times 100$$

$$\Rightarrow \frac{20}{100} = \frac{S.P - C.P}{C.P}$$

$$\Rightarrow S.P = 1.2\times C.P$$

$$\Rightarrow S.P = 62.5$$

So, to get a gain of 20% we need to sell each mango at Rs. 62.5 

Let say we sold 'x' number of mangoes.

Selling price of these 'x' number of mangoes (S.P) = Rs. 62.5x

But given that this S.P = Rs. 1000

$$\Rightarrow 62.5x = 1000$$

$$\Rightarrow x = \frac{1000}{62.5} = 16$$.

Therefore a total of 16 mangoes are to be sold for Rs. 1000 to get a gain of 20%.

Let the marked price of two balls be X

Given that they were bought at 37.40 rupees at 15% discount.

=> X x $$\ \frac{\ 85}{100}$$=37.40

X= 44
we have considered that the marked price of two balls is X i.e: 44 rupees.

The question is asking to find marked price of each ball

so, answer is 22 rupees

option B

Let say cost price(C.P) of 1 kg(1000 g) of rice be Rs. 100

Given Shopkeeper is selling rice  at cost price,

$$\Rightarrow$$ Selling price(S.P) = C.P = Rs. 100

If he had used correct weight of 1000 g then C.P would have also been Rs. 100.

But given that he uses false weight. Let the weight he had used be  'x' g.

For 1000 g of rice  the C.P = Rs. 100

$$\Rightarrow$$ For '1' g of rice the C.P will be Rs. $$\frac{1}{10}$$

$$\Rightarrow$$ For 'x' g of rice the C.P will be Rs. $$\frac{x}{10}$$

Given that, by using this false weight the shop keeper gains 20%.

Gain percentage = $$\frac{S.P - C.P}{C.P}\times 100$$

$$\Rightarrow \frac{20}{100} = \frac{S.P - C.P}{C.P}$$

$$\Rightarrow S.P = 1.2\times C.P$$

$$\Rightarrow 100 = 1.2\times \frac{x}{10}$$

$$\Rightarrow x = 833.33$$ 

Hence the false weight used is 833.33 g 

Initial price is given as 'I' = Rs. 600

After the first reduction, the initial price is reduced by 10%

$$\Rightarrow$$ the new price I' = $$600[1 - \frac{10}{100}] = 540$$

After second reduction, I' is reduced by 10%

$$\Rightarrow$$ the new price I'' = $$540[1 - \frac{10}{100}] = 486$$

After third reduction, I'' is reduced by 10%

$$\Rightarrow$$ the new price I''' = $$486[1 - \frac{10}{100}] = 437.4$$

Hence the Current price after three successive reductions is Rs. 437.4