Question

A producer of tea blends produces two varieties of tea from two tea gardens one costing Rs. 18 per Kg and another Rs. 20 per kg in the ratio x:y. If he sells the blended variety at Rs. 21 per kg. His gain percentage is 12 then ratio is:
$\left( A \right)3:5$
$\left( B \right)3:4$
$\left( C \right)5:3$
$\left( D \right)1:1$

Answer 1

Hint – In this particular question use the concept that the total cost price of the variety of tea is the summation of the product of amount of varieties and the respective ratio of the varieties and the total selling price is the product of the sum of the ratio multiplied by the selling price so use these concepts to reach the solution of the question.

Complete step-by-step answer:
Given ratio of two varieties of tea = x : y.
Now it is given that the cost of the first variety of tea = Rs. 18 per kg.
And the cost of the second variety of tea = Rs. 20 per kg.
Now the total cost price of the variety of tea is the summation of the product of the amount of varieties and the respective ratio of the varieties.
Therefore, total cost price (C.P) = $18x + 20y$
Now it is given that he sells the blended variety at Rs. 21 per kg.
So the total selling price is the product of the sum of the ratio multiplied by the selling price.
So, the total selling price (S.P) is = $\left( {x + y} \right)21$
Now as we know that the gain percentage is the ratio of the difference of the selling price and the cost price to the cost price multiplied by 100.
So gain percentage = $\dfrac{{{\text{S}}{\text{.P}} - {\text{C}}{\text{.P}}}}{{{\text{C}}{\text{.P}}}} \times 100$
Now the gain percentage = 12% (given)
Therefore, 12 = $\dfrac{{{\text{S}}{\text{.P}} - {\text{C}}{\text{.P}}}}{{{\text{C}}{\text{.P}}}} \times 100$
Now substitute all the values in the above equation we have,
Therefore, 12 = $\dfrac{{21\left( {x + y} \right) - \left( {18x + 20y} \right)}}{{\left( {18x + 20y} \right)}} \times 100$
Now simplify this we have,
Therefore, $216x + 240y = \left( {21x + 21y - 18x - 20y} \right) \times 100$
$ \Rightarrow 216x + 240y = 300x + 100y$
$ \Rightarrow 140y = 84x$
$ \Rightarrow \dfrac{x}{y} = \dfrac{{140}}{{84}} = \dfrac{{10}}{6} = \dfrac{5}{3}$
So this is the required ratio.
Hence option (C) is the required answer.

Note – Whenever we face such types of questions the key concept we have to remember is that the gain percentage is the ratio of the difference of the selling price and the cost price to the cost price multiplied by 100 (i.e. gain percentage = $\dfrac{{{\text{S}}{\text{.P}} - {\text{C}}{\text{.P}}}}{{{\text{C}}{\text{.P}}}} \times 100$), so first find out the total cost price and the selling price as above then substitute these value in the above formula and simplify we will get the required answer.