question_answer

Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2, If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be

A)  Rs. 169.50

B)  Rs. 170

C)  Rs. 175.50

D)  Rs. 180

Correct Answer: C

Solution :

[c] Since, first and second varieties are mixed in equal proportions, so their average price

\[=Rs.\,\,\left( \frac{126+135}{2} \right)=Rs.\,\,130.50\]

So the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e. 1 : 1. We have to find x.

By the rule of alligation, we have

\[\therefore \]\[\frac{x-153}{22.50}=1\]\[\Rightarrow \]\[x-153=22.50\]\[\Rightarrow \]\[x=175.50\]

Hence, price of the third variety is Rs. 175.50 per kg.