Question

In what ratio Darjeeling Tea costing $\text{Rs.}320$ per $\text{Kg}$ be mixed with Assam Tea costing $\text{Rs.}250$ per $\text{Kg}$ so that there is a gain of $20\%$ by selling the mixture at $\mathrm{Rs}.324$ per $\text{Kg}$.

• A. $1:2$
• B. $2:3$
• C. $3:2$
• D. $2:5$

Answer 1

The correct option is D

$2:5$

Compute the required ratio.

In the question, it is given that Darjeeling Tea costing $\text{Rs.}320$ per $\text{Kg}$ be mixed with Assam Tea costing $\text{Rs.}250$ per $\text{Kg}$ so that there is a gain of $20\%$ by selling the mixture at $\mathrm{Rs}.324$ per $\text{Kg}$.

$\text{Gain Percentage}=\frac{\mathrm{Selling}\mathrm{Price}-\mathrm{Cost}\mathrm{Price}}{\mathrm{Cost}\mathrm{Price}}$

Selling Price is $\text{Rs.}324$

$\text{Gain Percentage}$ = $20\%$

$$\begin{gathered} \frac{20}{100}=\frac{324-\mathrm{Cost}\mathrm{Price}}{\mathrm{Cost}\mathrm{Price}} \\ \Rightarrow \mathrm{Cost}\mathrm{Price}=\frac{324\times 100}{120} \\ \Rightarrow \mathrm{Cost}\mathrm{Price}=270 \end{gathered}$$

The suitable Price for Darjeeling Tea is $324-270=\text{Rs.}54$.

The suitable Price for Assam Tea is $270-250=\text{Rs}.20$.

So, the required ratio can be given as follows:

.$20:50=2:5$.

Therefore, the required ratio is $2:5$.

Hence, option (D) is the correct answer.