If the market price of a bag is 25% above the cost price, and a discount of 18% is declared on it, then find the gain percentage.

Correct — C. Take CP = ₹100. The discount comes off the marked price, not off the cost.

MP = 100 + 25% of 100 = ₹125
Discount = 18% of 125 = ₹22.50
SP = 125 − 22.50 = ₹102.50

Gain = 102.50 − 100 = ₹2.50 on a cost of ₹100 = 2.5% → option (c).

Why the others are wrong

• (a)
  1.5% — A 1.5% gain means SP = ₹101.50, which is a cut of ₹23.50 off ₹125 — that is a 18.8% discount, not the 18% the question gives.
• (b)
  3.0% — A 3% gain means SP = ₹103, a cut of only ₹22 off ₹125, i.e. a 17.6% discount. The stated 18% takes off ₹22.50.
• (d)
  2.0% — A 2% gain means SP = ₹102, a cut of ₹23 off ₹125, i.e. 18.4%, not 18%. It is also what the shortcut 25 − 18 − (25 × 18) ⁄ 100 returns if the correction term 4.5 is rounded to 5.

Mark-up and discount are percentages of different bases. The 25% mark-up is on the cost price; the 18% discount is on the marked price. Mixing the bases is the whole difficulty.

Assuming CP = ₹100 removes the algebra, because every percentage then reads directly in rupees. The chain is CP → MP → SP, and gain% is measured back against CP.

As a single step, a +25% then −18% chain combines to 25 − 18 − (25 × 18) ⁄ 100 = 7 − 4.5 = +2.5%. Equivalently, 1.25 × 0.82 = 1.025, a factor 2.5% above 1.

Key facts

• Marked price 25% above cost means MP = 1.25 × CP.
• A discount is always reckoned on the marked price, never on the cost price.
• Successive changes of a% and b% combine to a + b + ab/100, with a discount entering as a negative b.
• Gain% = (SP − CP) ÷ CP × 100, so the denominator is the cost price.

Common traps

• Subtracting the percentages to get 25 − 18 = 7%.
• Taking 18% off the cost price of ₹100 instead of off ₹125.
• Dividing the ₹2.50 profit by the selling price, which gives 2.44%.

No directly related past PYQ was found.