Question

A shopkeeper declares the following three schemes of discounts. Which scheme is most beneficial to a customer? A. Buy 25 items and get 30 of the same items B. Two successive discounts of 12% and 18% C. Two successive equal discounts of 15%

• A. A
• B. B and C
• C. Only C
• D. Only B

Answer 1

Answer:

B. B and C

Let’s compare all three schemes by converting them into effective discount %.

Buy 25 items, get 30 items

You pay for 25 items and get 30 items.

$\text{Effective price per item} = \frac{25}{30} = \frac{5}{6}$

$\text{Discount} = 1 - \frac{5}{6} = \frac{1}{6} = 16.67\%$

Successive discounts of 12% and 18%

Formula:
$\text{Net discount} = a + b - \frac{ab}{100}$
$= 12 + 18 - \frac{12 \times 18}{100}$
$= 30 - 2.16 = 27.84\%$

Two successive discounts of 15%

$= 15 + 15 - \frac{15 \times 15}{100}$
$= 30 - 2.25 = 27.75\%$
Final Comparison

• A = 16.67%

• B = 27.84% ✅ (Highest)

• C = 27.75%

Most beneficial scheme: B (12% and 18%)

It gives the maximum discount.