In what ratio must a grocer mix two varieties of cumin seeds worth Rs. 60 per kg and Rs. 65 per kg respectively, so that by selling the mixture at Rs. 68.20 per kg, he may gain 10%?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3:2
The selling price includes a gain of 10%, so the cost price of the mixture is
\( \displaystyle \text{CP of mixture}=\frac{68.20}{1.10}=\text{Rs. }62\ \text{per kg} \)
By the rule of alligation,
\( \displaystyle \frac{\text{Quantity at Rs. }60}{\text{Quantity at Rs. }65}=\frac{65-62}{62-60}=\frac{3}{2} \)
The varieties must be mixed in the ratio 3 : 2.
Why the other options are incorrect
Option (1) 1:3 — Incorrect. With 1 : 3 the cost price would be \( \frac{60+195}{4}=63.75 \), not 62.
Option (2) 3:1 — Incorrect. With 3 : 1 the cost price would be \( \frac{180+65}{4}=61.25 \), not 62.
Option (4) 2:3 — Incorrect. 2 : 3 is the alligation ratio taken the wrong way round; it gives a cost price of \( \frac{120+195}{5}=63 \), not 62.