In what ratio must a grocer mix two varieties of sugar A and B worth Rs. 40 per kg and Rs. 50 per kg respectively, so that by selling that mixture at Rs. 46.20 per kg, he may gain 10%?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 4:1
Selling at a 10% gain means SP = 1.1 × CP, so the cost price of the mixture is
\( \displaystyle \text{CP}=\frac{46.20}{1.1}=\text{Rs. }42\text{ per kg} \)
By the rule of alligation,
\( \displaystyle \frac{\text{quantity of A}}{\text{quantity of B}}=\frac{50-42}{42-40} \)
\( \displaystyle =\frac{8}{2}=\frac{4}{1} \)
So A and B are mixed in the ratio 4 : 1.
Shortcut: Check Option (1): \( \frac{4\times 40+1\times 50}{5}=\frac{210}{5}=42 \), and \( 42\times 1.1=46.20 \).
Why the other options are incorrect
Option (2) 1:4 — Incorrect. 1 : 4 reverses the ratio; it gives a mean price of \( \frac{40+200}{5}=48 \).
Option (3) 3:2 — Incorrect. 3 : 2 gives \( \frac{120+100}{5}=44 \), not 42.
Option (4) 2:3 — Incorrect. 2 : 3 gives \( \frac{80+150}{5}=46 \), which is close to the selling price 46.20 but is not the cost price 42.
Tip: Apply alligation to the cost price of the mixture, not to its selling price; using 46.20 directly is the trap here.