Question

The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs. 20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2:3, then the price per kg of the mixed variety of rice is:
A. Rs. 18
B. Rs. 18.50
C. Rs. 19
D. Rs. 19.50

Answer 1

Hint – In order to solve this problem we need to assume the variables and use the rule of allegation and then solve the equation formed to get the values of the variable and answer.

Complete step-by-step answer:
Let the price of the mixed variety be Rs. x per kg.
It is given that the cost of one Kg of Type 1 rice is 15 and that of type 2 is 20.
If various amounts of different ingredients are combined together to produce a mixture of a mean value, the ratio of their amount is inversely proportional to the difference in their expense from the mean value.

By the rule of allegation, we have:

We have to divide type 1 and type 2 rice in a 2:3 ratio.
$\dfrac{{{\text{20 - x}}}}{{{\text{x - 15}}}}{\text{ = }}\dfrac{{\text{2}}}{{\text{3}}}$
On solving t further we get,
60−3x=2x−30
5x=90
x=18.
So, we get the value of x as 18.
So, the price per kg of the mixed variety of rice is Rs.18.
Hence, the correct option is A.

Note – When you get to solve such problems of ratio, always remember that we have to make equations using fractions and getting the values of variables. Then we have to solve the fraction to get the value of the variable. We need to take care of solving the algebraic equations. We need to know that if various amounts of different ingredients are combined together to produce a mixture of a mean value, the ratio of their amount is inversely proportional to the difference in their expense from the mean value.