Question

If a commission $15$% given on the marked price of a book, the publisher gain $19$%. If the commission is not there, the gain of publisher is

• A. $30$%
• B. $20$%
• C. $40$%
• D. $50$%

Answer 1

The correct option is C $40$%

Cost price=CP, Selling price=SP

Marked Price=MP

If $15$% commission on MP is given

$SP=MP-\frac{15}{100}MP=\frac{85}{100}MP\to 1$

Under this condition gain is $19$%

$SP=CP+\frac{19}{100}CP=\frac{119}{100}CP\to 2$

If there is no commission

$S{P}^1=MP$ (MP and CP will not change)

But from $1$ and $2$

$\frac{85}{100}MP=\frac{119}{100}CP$

$MP=\frac{119}{85}CP$

$S{P}^1=MP=\frac{119}{100}CP=\left(\frac{85+34}{85}\right)CP$

$S{P}^1=CP=\frac{34}{85}CP=CP+\frac{2}{5}CP$

$=CP+40$% of CP

$\therefore$ Gain for publisher is $40$%