After offering two successive discounts a toy with a marked price of ₹150 is sold at ₹105. If the value of the first discount is 12.5%, what is the value of the second discount?

Correct — B. Successive discounts apply one after the other, each to the price that survived the previous cut.

First discount 12.5% = 1⁄8, so
150 × (1 − 1⁄8) = 150 × 7⁄8 = ₹131.25

The second cut must take ₹131.25 down to ₹105:
105 ⁄ 131.25 = 0.8, so 20% has been knocked off.

Second discount = 20% → option (b).

Why the others are wrong

• (a)
  18% — Too shallow. 18% off ₹131.25 leaves about ₹107.63, and the toy actually sold for ₹105.
• (c)
  21% — Too deep. 21% off ₹131.25 leaves about ₹103.69, more than a rupee under the stated selling price.
• (d)
  22% — Deeper still. 22% off ₹131.25 leaves about ₹102.38 — nearly ₹3 below the ₹105 the question fixes.

Successive discounts multiply, they do not add. Cuts of x% and y% leave (1 − x⁄100)(1 − y⁄100) of the marked price, so the single equivalent discount is x + y − xy⁄100.

The overall cut here is already visible: 105 ⁄ 150 = 0.7, so 30% in total.

That opens a one-line route from the other end: 0.7 ⁄ 0.875 = 0.8, again a 20% second discount. The formula agrees — 12.5 + 20 − 2.5 = 30.

Key facts

• Successive discounts of x% and y% leave (1 − x⁄100)(1 − y⁄100) of the marked price.
• The single discount equivalent to x% then y% is x + y − xy⁄100, which makes 12.5% and 20% together a 30% cut.
• 12.5% is 1⁄8 and 20% is 1⁄5, so ₹150 falls to ₹131.25 and then to ₹105.

Common traps

• Adding the rates and answering 17.5%, as if 12.5% plus the second cut made 30%
• Taking the second discount on the marked price ₹150 rather than on ₹131.25
• Rounding 12.5% to 12% and losing the clean 1⁄8 fraction

No directly related past PYQ was found.