In what ratio must a shopkeeper mix two types of oranges worth Rs. 55 per kg and Rs. 70 per kg respectively so as to get a mixture at Rs. 65 per kg.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1 : 2
By the rule of alligation:
\( \displaystyle \frac{\text{Quantity of cheaper}}{\text{Quantity of dearer}} = \frac{\text{Price of dearer} - \text{Mean price}}{\text{Mean price} - \text{Price of cheaper}} \)
\( \displaystyle = \frac{70 - 65}{65 - 55} = \frac{5}{10} = \frac{1}{2} \)
So the oranges at Rs. 55 and Rs. 70 per kg are mixed in the ratio 1 : 2.
Check: 1 kg at Rs. 55 and 2 kg at Rs. 70 cost Rs. 195 for 3 kg, that is Rs. 65 per kg.