If a commission at the rate of 10% is given to a bookseller on the marked price of a book by the publisher, the publisher gains 20% . If the commission is increased to 15% , then the gain percent would be = ?

A. $$6\frac{2}{3}\% $$

B. $$13\frac{1}{3}\% $$

C. $$15\frac{5}{6}\% $$

D. $$12\frac{1}{2}\% $$

Answer: Option B

Solution(By Examveda Team)

Let CP = 100 and Marked Price = x
SP = 100 + 20% of 100 = 120
10% commision was given on SP
SP = x - 10% of x
$$\eqalign{ & 120 = x - \frac{{10x}}{{100}} \cr & 120 = \frac{{9x}}{{10}} \cr & 9x = 1200 \cr & x = \frac{{1200}}{9} = 133.33 \cr & {\text{MP}} = 133.33 \cr} $$
If 15% commission was given, then
SP = 133.33 - 15% of 133.33
SP = 133.33 - 20
SP = 113.33
Gain = 113.33 - 100
% Gain = 13.33% or $$13\frac{1}{3}\% $$