Question

In what ratio must a grocer mix two varieties of pulses costing Rs.15 and Rs.20 per kg respectively so as to get a mixture worth Rs.16.50 per kg?
A.3:7
B.5:7
C.7:3
D.7:5

Answer 1

Hint: Assume x kg from pulse costing Rs.15 per kg and y kg from pulse costing Rs.20 per kg is mixed to get the mixture which has cost Rs.16.50 per kg. Use the variables x and y and the data given in the question to derive an expression for the cost per kg of the mixture. Equate this with the given cost and solve for x and y to find their ratio.

Complete step-by-step answer:
Cost of x kg of pulse having cost Rs.15 per kg= Rs.15x.
Cost of y kg of pulse having cost Rs.20 per kg= Rs.20y.
The total cost of the mixture having both varieties of pulses= Rs.(15x+20y).
Total weight of the mixture=(x+y)kg.
Cost of mixture per kg = \[\dfrac{15x+20y}{x+y}\]
According to the question, it is given that the mixture costs Rs.16.50 per kg.
\[\dfrac{15x+20y}{x+y}=16.50\]
\[\begin{align}
  & \dfrac{15x+20y}{x+y}=16.50 \\
 & \Rightarrow 2(15x+20y)=33(x+y) \\
 & \Rightarrow 30x+40y=33x+33y \\
 & \Rightarrow 40y-33y=33x-30x \\
 & \Rightarrow 7y=3x \\
 & \Rightarrow \dfrac{7}{3}=\dfrac{x}{y}. \\
\end{align}\]
Thus the required ratio is 7:3.

Note: The other way to solve this question is to go through the options given. For example, one option has a ratio of 7:3. Just take 10kg of mixture where 7 kg pulse is of Rs.15 per kg and 3 kg pulse is of Rs.20 per kg. Calculate per kg cost of pulse and if it matches Rs.16.5 then that option is correct.