The marked price of a bed sheet is ₹500. At the time of its sale, two successive discounts of 10% and 5% are available. Find the selling price (in ₹) of the bed sheet.

Correct — A. Successive discounts are applied one after the other, each to the price left after the previous cut.

After 10% off ₹500: 500 × 90⁄100 = ₹450
After 5% off ₹450: 450 × 95⁄100 = ₹427.50

Selling price = ₹427.50 → option (a).

As a single cut the pair removes 100 − (0.9 × 0.95 × 100) = 14.5%, not 15%.

Why the others are wrong

• (b)
  430.00 — ₹430 is a flat 14% off ₹500. The two cuts here remove 14.5%, half a percentage point more, so ₹430 is ₹2.50 too high.
• (c)
  445.00 — ₹445 is only 11% off ₹500, a discount of ₹55. The stated cuts take ₹72.50 off, leaving ₹17.50 less than this.
• (d)
  432.50 — ₹432.50 is 13.5% off ₹500. The second cut has to take 5% of the ₹450 that remains, which is ₹22.50, and this option is ₹5 short of that.

Discounts multiply, they do not add. Two successive cuts of a% and b% leave a factor of (1 − a⁄100)(1 − b⁄100) of the marked price.

Here that factor is 0.9 × 0.95 = 0.855, so ₹500 becomes ₹427.50.

The equivalent single discount is a + b − ab⁄100 = 10 + 5 − 0.5 = 14.5%. The small −ab⁄100 term is the part candidates drop, and it is exactly the 0.5% that separates two of the options here.

Key facts

• Selling price after successive discounts = MP × (1 − d₁⁄100) × (1 − d₂⁄100).
• Discounts of a% and b% are equal to one discount of a + b − ab⁄100 per cent.
• Ten per cent then five per cent leaves 85.5% of the marked price.

Common traps

• Adding the two percentages to 15% and computing ₹425.
• Taking the second discount on the marked price instead of on the ₹450 that remains.
• Rejecting ₹427.50 because the other options are whole rupees.

No directly related past PYQ was found.