Question

In what ratio must tea at Rs. $62$ per kg be mixed with tea at Rs. $72$ per kg so that the mixture must. be worth Rs. $64.50$ per kg?

Answer 1

Let the quantity of the tea that is $Rs.62$ per kg be $x$ kg and that of tea that is $Rs.72$ per kg be $y$ kg.

Hence, the required ratio is $x:y$.

Price of $x$ kg tea $=Rs.62x$

Price of $y$ kg tea $=Rs.72y$

If we mix both varieties of tea, the quantity of the mixture will be $x+y$.

Now, this mixture is $Rs.64.50$ per kg.

Hence, the total price of mixture $=Rs.64.50(x+y)$

So, $62x+72y=64.50(x+y)$

$\Rightarrow 62x+72y=64.5x+64.5y$

$\Rightarrow 64.5x-62x=72y-64.5y$

$\Rightarrow 2.5x=7.5y$

$\Rightarrow \frac{x}{y}=\frac{7.5}{2.5}$

$\Rightarrow \frac{x}{y}=3$

So, $x:y=3:1$

Hence, the required ratio is $3:1$.