A shopkeeper mixes two varieties of pulses – one costing ₹80 per kg and the other costing ₹100 per kg, in the ratio 3 : 1. If he sells the mixed variety at ₹91.80 per kg, find his gain or loss percent.

Correct — C. Find the cost of 1 kg of the mixture, then compare it with the selling price.

Take 3 kg at ₹80 and 1 kg at ₹100.
Cost of 4 kg: 3 × 80 + 1 × 100 = ₹340
Cost per kg: 340 ÷ 4 = ₹85

Gain per kg: 91.80 − 85 = ₹6.80
Gain% on cost: 6.80 ÷ 85 × 100 = 8% gain → option (c)

Why the others are wrong

• (a)
  8% Loss — 8% Loss has the right size but the wrong direction. The selling price, ₹91.80, is above the ₹85 cost, so the shopkeeper gains. An 8% loss would mean selling at ₹78.20.
• (b)
  10% Gain — 10% Gain would need a selling price of 85 × 1.10 = ₹93.50. At ₹91.80 the gain is ₹6.80 on a cost of ₹85, which is 8%.
• (d)
  10% Loss — 10% Loss would need a selling price of 85 × 0.90 = ₹76.50. The actual price, ₹91.80, is above cost, so there is no loss at all.

The cost of a mixture is the weighted average of its parts, weighted by quantity: (3 × 80 + 1 × 100) ÷ 4 = ₹85 a kg. Three of every 4 kg are the cheaper pulse, so the cost sits nearer ₹80 than ₹100.

After that it is plain profit and loss. Compare the selling price with the cost, and state the gain as a percentage of cost, not of the selling price.

Key facts

• Cost per kg of a mixture = (q₁ × c₁ + q₂ × c₂) ÷ (q₁ + q₂).
• Gain% = (selling price − cost price) ÷ cost price × 100.
• A 3 : 1 mix of ₹80 and ₹100 pulses costs ₹85 a kg, a quarter of the way from 80 to 100.

Common traps

• Averaging ₹80 and ₹100 to ₹90 and ignoring the 3 : 1 ratio, which gives a 2% gain.
• Dividing the ₹6.80 gain by the selling price, ₹91.80, which gives about 7.4%. Gain% is on cost.

No directly related past PYQ was found.