# Profit and Loss Questions

Q:

A milkman purchases the milk at Rs. x per litre and sells it at Rs. 2x per litre still he mixes 2 litres water with every 6 litres of pure milk. What is the profit percentage?

 A) 116% B) 166.66% C) 60% D) 100%

Explanation:

Let the cost price of 1 litre pure milk be Re.1, then

$\inline&space;\begin{Bmatrix}&space;6&space;&&space;litres(milk)&space;&&space;\rightarrow&space;&&space;CP=Rs.6\\&space;2&space;&&space;litres(water)&space;&&space;\rightarrow&space;&&space;CP=Rs.0&space;\end{Bmatrix}\rightarrow&space;CP=Rs.6&space;only$

and 8 litre mixture  $\rightarrow$ SP $\rightarrow$ 8 x 2 = Rs.16

Profit %= $\inline \left [ \frac{\left ( 16-6 \right )}{6} \right ]\times 100=\frac{1000}{6}=166.66$%

118 17797
Q:

A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:

 A) No profit, no loss B) 5% C) 8% D) 10%

Explanation:

C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.

S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.

Gain =${\color{Black}&space;\left&space;(&space;\frac{80}{1600}&space;\times&space;100\right&space;)&space;}$% = 5%

111 15086
Q:

By selling 45 lemons for Rs 40, a man loses 20 %. How many should he sell for Rs 24 to gain 20 % in the transaction ?

 A) 16 B) 18 C) 20 D) 22

Explanation:

Let S.P. of 45 lemons be Rs. x.

Then, 80 : 40 = 120 : x or   x = $\inline \frac{40\times 120}{80}$= 60

For Rs.60, lemons sold = 45

For Rs.24, lemons sold  =$\inline \frac{45}{60}\times 24$= 18.

124 14354
Q:

A shopkeeper cheats to the extent of 10% while buying and selling, by using false weights. His total gain is.

 A) 20% B) 21% C) 22% D) 23%

Explanation:

Gain % = $\inline&space;\fn_jvn&space;{\color{Black}&space;(\frac{(100+common\;&space;gain\;&space;percent)^{2}}{100}-100)}$%

= $\inline&space;\fn_jvn&space;{\color{Black}&space;(\frac{(100+10)^{2}}{100}-100)}$%

= $\inline&space;\fn_jvn&space;{\color{Black}&space;(\frac{12100-10000}{100})}$%

= 21%

60 11216
Q:

The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:

 A) 15 B) 16 C) 18 D) 25

Explanation:

Let C.P. of each article be Re. 1 C.P. of x articles = Rs. x.

S.P. of x articles = Rs. 20.

Profit = Rs. (20 - x).

${\color{Black}&space;\therefore&space;\left&space;(&space;\frac{20-x}{x}\times&space;100=25&space;\right&space;)}$

$\inline \fn_jvn \Rightarrow$2000 - 100x = 25x

$\inline \fn_jvn \Rightarrow$125x=2000

$\inline \fn_jvn \Rightarrow$x=16