A bookseller can gain 6.666% if he offers a 20% commission on the written selling price of a book. If the commission is reduced to 10% , what will be his gain ?
A
15%
B
10%
C
20%
D
25%
Correct Answer: 20%
Let the actual and written price be A and S respectively. Selling price at 6.666% gain = A + 6.666% of A = 1.0666A Selling price at 20% commission or written price = S - 20% of S = S - 0.2S = 0.8S Selling price at 6.666% gain = Selling price at 20% commission on written price or, 1.066A = 0.8S or, S = 1.066A/0.8 = 1.33325A Selling price at 10% commission = S - 10% of S = S - 0.1S = 0.9S So, gain at 10% commission on written price = (0.9S - A) / A x 100% = (0.9 ×1.33325A - A) / A × 100% = (1.2A - A) / A × 100% = 0.2 × 100% = 20%