The difference between a discount of 25% and two successive discounts of 15% and 10% on a certain bill was Rs. 25. Find the amount of the bill.

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 03 Dec 2022 Shift 1)

Answer 1

Given:

Single Discount = 25%

Successive Discount = 15% and 10%

Difference = Rs. 25

Calculation:

Let the bill amount be Rs. 100x.

Case 1:

25% discount to the 100x = 25x discount

Price after discount = 100x - 25x

⇒ 75x

Case 2:

Discount of 15% to the 100x = 15x

Price after discount = 100x - 15x

⇒ 85x

Second Discount of 10% to the 85x = 8.5x

Price after the second discount = 85x - 8.5x

⇒ 76.5x

According to the question,

76.5x - 75x = 25

⇒ 1.5x = 25

⇒ x = 25/1.5

⇒ x = 16.6667

⇒ 100x = Rs.1666.67

∴ The bill amount is of Rs.1,666.67.

Shortcut Trick

Two successive discounts of 15% and 10% are equivalent to 15 + 10 - (15 × 10)/100 = 23.5%

So, the difference between the two discounts (25 - 23.5) = 1.5%

Now, 1.5% → 25

Then, 100% → 25/1.5 × 100 = 1666.67