A grocer mixes two varieties of rice – one costing ₹40 per kg and the other costing ₹60 per kg, in the ratio 2 : 3. If he sells the mixed variety at ₹57.20 per kg, find his gain or loss percent.
- (a)10% Loss
- (b)10% Gain
- (c)8% Gain
- (d)8% Loss
Answer
Why
Correct — B.
Cost of 2 kg at ₹40: 2 × 40 = ₹80
Cost of 3 kg at ₹60: 3 × 60 = ₹180
Cost of the 5 kg mixture: 80 + 180 = ₹260
Cost price per kg: 260 ÷ 5 = ₹52
Gain per kg: 57.20 − 52 = ₹5.20
Gain %: 5.20 ÷ 52 × 100 = 10%
The selling price is above cost, so it is a 10% Gain → option (b)
Why the others are wrong
- (a)10% Loss — Right size, wrong direction. Selling at ₹57.20 is above the ₹52 cost, so the grocer gains. A loss needs a selling price below ₹52.
- (c)8% Gain — An 8% gain means selling at ₹56.16 (52 × 1.08). The grocer sells at ₹57.20, a gain of ₹5.20 on ₹52, which is 10%.
- (d)8% Loss — Wrong direction and wrong size. An 8% loss means selling at 52 × 0.92 = ₹47.84, but ₹57.20 is above the cost.
Concept
A mixture's cost price is the weighted average of its ingredients' prices, weighted by quantity: (q₁c₁ + q₂c₂) ÷ (q₁ + q₂).
With the ratio 2 : 3, take 2 kg and 3 kg. The weights matter: the plain average of ₹40 and ₹60 is ₹50, but more of the dearer rice pulls the cost up to ₹52.
Gain or loss is then worked on that cost, as for any single article.
Key facts
- Mixture cost per kg = total cost ÷ total quantity
- Rice at ₹40 and ₹60 mixed 2 : 3 costs ₹52 per kg
- Gain % = (SP − CP) ÷ CP × 100, taken on the cost price
Study next
Common traps
- Averaging ₹40 and ₹60 to ₹50 and ignoring the 2 : 3 ratio, which gives a 14.4% gain
- Dividing the ₹5.20 gain by the selling price ₹57.20 instead of the cost price ₹52
13 Sep 2025, 16:00, Quant Q.4 and 17 Sep 2025, 12:30, Quant Q.3 use this template with other numbers, keyed 5% Loss and 8% Gain.
15 Sep 2025, 16:00, Quant Q.15 runs it in reverse, giving the mixture price and asking one ingredient's cost, keyed ₹114.
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