Arithmetic

Profit & Loss

Hard

A man buys $35$ kg of sugar and sets a marked price in order to make a $20\%$ profit. He sells $5$ kg at this price, and $15$ kg at a $10\%$ discount. Accidentally, $3$ kg of sugar is wasted. He sells the remaining sugar by raising the marked price by $p$ percent so as to make an overall profit of $15\%$ . Then $p$ is nearest to

$25$

$22$

$31$

$35$

✅ Correct Option: 1

A shopkeeper buys sugar, sets a marked price for profit, sells at different rates, has some wastage, and needs to find what percentage increase is needed on the remaining stock to achieve his target profit.

Key insight: We need to work backwards from the desired overall profit to find the required price increase.

Let's assume the cost price per kg = ₹1 (this makes calculations easier without losing accuracy)

Since he wants 20% profit on marked price:

Marked Price = ₹1.2 per kg

Total cost for 35 kg = 35 × ₹1 = ₹35

For 15% overall profit:

Target Total Revenue = 35 × 1.15 = ₹40.25

This is the total amount he needs to collect from all sales to achieve 15% profit

Let's track what happens to each portion of the 35 kg:

Category 1: 5 kg sold at marked price

Revenue = 5 × ₹1.2 = ₹6

Category 2: 15 kg sold at 10% discount

Selling price per kg = ₹1.2 × (1 - 0.10) = ₹1.2 × 0.9 = ₹1.08

Revenue = 15 × ₹1.08 = ₹16.2

Category 3: 3 kg wasted

Revenue = ₹0

Category 4: Remaining sugar

Remaining quantity = 35 - 5 - 15 - 3 = 12 kg

This needs to be sold at marked price + p% increase

Total Revenue = Revenue from all categories

₹6 + ₹16.2 + ₹0 + (Revenue from 12 kg) = ₹40.25

Revenue from 12 kg = ₹40.25 - ₹6 - ₹16.2 = ₹18.05

For 12 kg to generate ₹18.05:

Selling price per kg = ₹18.05 ÷ 12 = ₹1.504

Since this is sold at marked price + p% increase:

₹1.2 × (1 + $\tfrac{p}{100}$ ) = ₹1.504

(1 + $\tfrac{p}{100}$ ) = 1.504 ÷ 1.2 = 1.253

Therefore: $\tfrac{p}{100}$ = 1.253 - 1 = 0.253

p = 25.3

The value of p is nearest to 25.

Why this approach works: By assuming cost price = ₹1, we simplified calculations without affecting the percentage relationships. The key insight is that we worked backwards from the target profit to find exactly how much revenue the remaining stock must generate.

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