Question

The cost price of two books is in the ratio of 2 ∶ 3. Marked price of books is 30% and 40% more than the cost price of books respectively. Each book is given after two successive discounts of 20%. The overall loss percentage incurred on the sale of the two books is ________

1. 13.40%
2. 11.84%
3. 11.50%
4. 12.96%

Answer 1

Correct Answer - Option 4 : 12.96%

Given:

The cost price of the two books is in the ratio of 2 ∶ 3.

Marked price over cost price is 30% and 40% for the respective books.

Each book is given after successive discounts of 20%.

Concepts used:

M.P. = S.P. + Discount

Discount % = Discount/M.P. × 100

Calculation:

Let cost price of two books be 2x and 3x.

⇒ Total C.P. of 2 books = 2x + 3x = 5x

⇒ M.P. of 1^st book = 2x + (2x × 30%) = 13x/5

⇒ M.P. of 2^nd book = 3x + (3x × 40%) = 21x/5

Each book is given after successive discounts of 20%.

⇒ First successive discounts on 1^st book = 13x/5 × 20% = 13x/25

⇒ Second successive discount on 1^st book = (13x/5 – 13x/25) × 20% = 52x/125

⇒ S.P. of 1^st book = 13x/5 – (13x/25) – (52x/125) = 208x/125

⇒ First successive discounts on 2^nd book = 21x/5 × 20% = 21x/25

⇒ Second successive discount = (21x/5 – 21x/25) × 20% = 84x/125

⇒ S.P. of 2^nd book = 21x/5 – (21x/25) – (84x/125) = 336x/125

⇒ Total S.P. = 208x/125 + 336x/125 = 544x/125

As C.P. > S.P.

⇒ Overall loss % = (5x – 544x/125)/5x × 100 = 12.96%

∴ Overall loss % is equal to 12.96%.