The ratio in which a grocer must mix two varieties of rice worth Rs. 56/kg and Rs. 62/kg so that he sells the mixture at Rs. 66/kg, making a profit of 10%, is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1 : 2
The mixing ratio depends on the cost price of the mixture, not its selling price. With a 10% profit,
\( \displaystyle \text{CP of mixture}=\frac{66}{1.10}=\text{Rs. }60\text{ per kg} \)
By the rule of alligation:
\( \displaystyle \frac{\text{quantity of cheaper}}{\text{quantity of dearer}}=\frac{62-60}{60-56} \)
\( \displaystyle =\frac{2}{4}=\frac{1}{2} \)
So the rice at Rs. 56/kg and at Rs. 62/kg are mixed in the ratio 1 : 2.
Shortcut: Check the average cost for each option ratio (56 : 62): only 1 : 2 gives Rs. 60.
\( \displaystyle 1:2\ \Rightarrow\ \frac{56+124}{3}=60 \)
\( \displaystyle 2:3\ \Rightarrow\ \frac{112+186}{5}=59.6 \)
\( \displaystyle 2:5\ \Rightarrow\ \frac{112+310}{7}\approx 60.29 \)
\( \displaystyle 5:2\ \Rightarrow\ \frac{280+124}{7}\approx 57.71 \)
Tip: The mean price must lie between the two prices; Rs. 66 does not, which shows at once that the selling price has to be converted to cost price first.