The cost price of a bat is 75% of the marked price. Calculate the gain percentage after allowing a discount of 15%.

Correct — D. The four options are printed as images; option (d) reads 13.33%.

Take the marked price as 100, since every figure in the question is a percentage of it.

CP = 75% of MP = 75
Discount 15% → SP = 100 − 15 = 85
Gain = SP − CP = 85 − 75 = 10

Gain% = gain ÷ CP × 100
= 10 ÷ 75 × 100 = 40⁄3 ≈ 13.33% → option (d).

Why the others are wrong

• (a)
  Option (a) shows 18.16%. Gain% is measured on the cost price 75, and 18.16% of 75 is a profit of 13.6 — but SP 85 minus CP 75 leaves a profit of only 10.
• (b)
  Option (b) shows 25.6%. A gain of 25.6% on CP 75 puts the selling price at 94.2, which is a discount of under 6% on the marked price. The question fixes the discount at 15%.
• (c)
  Option (c) shows 21.33%. That gain on CP 75 puts the selling price at 91, i.e. a discount of only 9%. With the stated 15% discount, SP is 85 and the profit cannot exceed 10.

When a question ties the cost price to the marked price by a percentage, set MP = 100. Every other figure then falls out as a plain number and no algebra is needed.

Discount is always taken off the marked price. Gain or loss is always measured on the cost price. Those two bases are different, and mixing them is the commonest error in this topic.

Here MP 100 gives CP 75 and SP 85, so a profit of 10 sits on a base of 75 — not on 100, not on 85.

Key facts

• Gain% is measured on the cost price, never on the marked price and never on the selling price.
• Setting MP = 100 turns "CP is 75% of MP" into CP = 75 and "discount 15%" into SP = 85.
• With CP = k × MP and discount d, gain% = (1 − d − k) ÷ k × 100, which here is 0.10 ÷ 0.75 × 100.

Common traps

• Dividing the profit of 10 by 100 or by 85 instead of by the cost price 75.
• Reading "75% of the marked price" as a 75% markup on cost.
• Subtracting 15 from the 25-point gap between MP and CP, getting 10, and calling it 10%.

No directly related past PYQ was found.