A shopkeeper marks his goods at 60% above the cost price. He allows a discount of 25% on the marked price. If he also gives an additional cash discount of ₹150, and still makes a profit of 14% on the cost price, what is the cost price of the goods?

Correct — B. Let the cost price be C.

Marked price = 60% above cost = 1.6C
After the 25% discount: 0.75 × 1.6C = 1.2C
After the ₹150 cash discount: selling price = 1.2C − 150

A 14% profit means selling price = 1.14C
So 1.2C − 150 = 1.14C → 0.06C = 150 → C = ₹2500 → option (b)

Why the others are wrong

• (a)
  ₹2000 — At ₹2000: marked ₹3200, 25% off gives ₹2400, less ₹150 is ₹2250 — a profit of ₹250, only 12.5% of cost, not 14%.
• (c)
  ₹3000 — At ₹3000: marked ₹4800, 25% off gives ₹3600, less ₹150 is ₹3450 — a profit of ₹450, which is 15% of cost, not 14%.
• (d)
  ₹3500 — At ₹3500: marked ₹5600, 25% off gives ₹4200, less ₹150 is ₹4050 — a profit of ₹550, about 15.7% of cost, not 14%.

Percentage discounts scale with the price, but a flat cash discount does not. That fixed ₹150 is what makes the cost price solvable.

After the mark-up and the 25% discount the price is 1.2C, 20% above cost. The 14% profit says the final price is 1.14C.

The gap between them, 0.06C, is exactly the ₹150 cash discount. So ₹150 is 6% of cost, and cost = 150 ÷ 0.06 = ₹2500.

Key facts

• A 60% mark-up followed by a 25% discount leaves the price at 1.6 × 0.75 = 1.2 times cost.
• Here the ₹150 cash discount equals the gap between 20% and 14% above cost, which is 6% of cost.
• If 6% of a number is 150, the number is 150 ÷ 0.06 = 2500.

Common traps

• Treating 60% − 25% = 35% as the net mark-up: 1.6 × 0.75 = 1.2, a net mark-up of 20%.
• Taking the ₹150 off the marked price before the 25% discount, although the stem applies the 25% to the marked price and the ₹150 on top of it.

No directly related past PYQ was found.