A sewing machine with a marked price of Rs.400 was being sold at a 10% discount for cash payment, and during the stock clearance, a further discount was offered such that the machine is sold at Rs.342. What was the second discount offered?

Given:

Marked Price (MP) = ₹400

First Discount = 10%

Final Selling Price (SP) = ₹342

Formula Used:

Selling Price after first discount (SP1) = MP × (1 - First Discount%/100)

Selling Price after second discount (SP) = SP1 × (1 - Second Discount%/100)

Calculation:

Selling Price after the first 10% discount:

SP1 = 400 × (1 - 10/100) = SP1 = 400 × (1 - 0.1) = ₹360

The machine was sold at ₹342 after a further discount on ₹360.

Let the second discount percentage be x%.

Final SP = SP1 × (1 - x/100)

342 = 360 × (1 - x/100)

⇒ 342 / 360 = 1 - x/100

⇒ 171 / 180 = 1 - x/100

⇒ 57 / 60 = 1 - x/100

⇒ x/100 = 1 - 19/20

⇒ x = (1 / 20) × 100

⇒ x = 5%

∴ The second discount offered was 5%.

Alternate Method

Formula used:

Second Discount = \(\dfrac{\text{Price after First Discount} - \text{Final Selling Price}}{\text{Price after First Discount}}\)

Calculation:

Price after First Discount = ₹400 - (10% of ₹400) = ₹400 - ₹40 = ₹360

Second Discount = \(\dfrac{₹360 - ₹342}{₹360}\)

⇒ Second Discount = \(\dfrac{₹18}{₹360}\)

⇒ Second Discount = 0.05

∴ The correct answer is option (2).