If a shopkeeper sells sugar at ₹44.8 per kg, he is able to make a 12% profit. Due to water seepage, 1⁄5 of the sugar is damaged. What should now be the selling price per kg of the rest of the sugar to have a 5% profit?

Correct — C. Start at the cost, not at the ₹44.8 selling price.

12% profit means SP = 1.12 × CP
CP = 44.8 ⁄ 1.12 = ₹40 per kg

Take 5 kg, so the damaged 1⁄5 is a whole kilogram.
Outlay = 5 × 40 = ₹200
Damaged = 1 kg, so only 4 kg are left to sell.

The 5% profit is on the ₹200 he spent, not on the 4 kg that survived.
Revenue needed = 200 × 1.05 = ₹210
New rate = 210 ⁄ 4 = ₹52.5 → option (c)

Why the others are wrong

• (a)
  ₹49.5 — ₹49.5 brings in 4 × 49.5 = ₹198 against a ₹200 outlay — a loss. Any rate under ₹50 fails before the 5% is even tested.
• (b)
  ₹51.5 — ₹51.5 yields 4 × 51.5 = ₹206, a gain of ₹6 on ₹200. That is 3%, not 5% — close enough to survive a rushed eyeball, which is the point of it.
• (d)
  ₹48.5 — ₹48.5 returns 4 × 48.5 = ₹194 on a ₹200 outlay, a ₹6 loss. The surviving 4 kg have to pay for all 5, and this rate does not manage it.

Profit is measured on what was spent, and spoilage does not refund anything. The money for all 5 kg is gone; only 4 kg can now earn it back.

So the useful number is the new break-even rate: ₹200 of cost spread over 4 saleable kg is ₹50 per kg. Losing a fifth of the stock has lifted break-even from ₹40 to ₹50.

The demanded 5% then rides on that: 50 × 1.05 = ₹52.5. Reading it this way makes the answer one multiplication instead of three.

Key facts

• A 12% profit means SP = 1.12 × CP, so ₹44.8 per kg corresponds to a cost of ₹40 per kg.
• Losing 1⁄5 of the stock raises the break-even rate from ₹40 to ₹50 per kg.
• ₹52.5 is exactly 5% above that ₹50 break-even.

Common traps

• Taking the 5% on the ₹44.8 selling price instead of on the cost.
• Charging 5% above ₹40 to get ₹42 and forgetting the kilogram that earns nothing.
• Spreading the recovered cost over 5 kg when only 4 kg are saleable.

No directly related past PYQ was found.