Question

In some quantity of ghee, 60% is pure ghee and 40% is vanaspati. If 10kg of pure ghee is added, then the strength of the vanaspati ghee becomes 20%. The original quantity was
(A) 10 kg
(B) 15 kg
(C) 20 kg
(D) 25 kg

Answer 1

- Hint: First assume the original quantity of ghee as $x$ and then find the strength of the vanaspati ghee after adding $10$kg of pure ghee. Solve the obtained equation to get the desired result.

Complete step-by-step solution:
It is given that $60\% $of ghee is pure and $40\% $is vanaspati ghee in some quantity of ghee. It is also given that vanaspati ghee becomes $20\% $, if we add more $10$ kg of pure ghee.
The goal is to find the original quantity of the ghee.
First assume that the original quantity of the ghee is $x$ kg.
Then, the quantity of vanaspati ghee is given as:
$40\% {\text{ of }}x = \dfrac{{40x}}{{100}}$
$40\% {\text{ of }}x = \dfrac{{2x}}{5}$
It is given that, after adding the $10$kg more pure ghee, the vanaspati ghee becomes $20\% $.
After adding $10$ kg more pure ghee, the amount of ghee becomes $\left( {x + 10} \right)$kg.
Then the strength of the vanaspati pure ghee after adding 10 kg of pure ghee is given as:
Strength of pure ghee$ = \dfrac{{40\% {\text{ of }}x}}{{{\text{Total amount of ghee}}}}$
Strength of pure ghee$ = \dfrac{{\left( {\dfrac{{2x}}{5}} \right)}}{{x + 100}}$
Substitute the strength of ghee as $20\% $, which is given in the problem, then we have
$20\% = \dfrac{{\left( {\dfrac{{2x}}{5}} \right)}}{{x + 100}}$
Solve the above equation for the value of $x$:
$\dfrac{{20}}{{100}} = \dfrac{{\left( {\dfrac{{2x}}{5}} \right)}}{{x + 10}}$
Simplifying the above equation,we get
$\dfrac{1}{5} = \dfrac{{2x}}{{5\left( {x + 10} \right)}}$
Solving for $x$ from the above equation,
$x + 10 = 2x$
$2x - x = 10$
On performing simple subtraction, we get
$x = 10$
We got the value of $x$ as 10, therefore the original quantity of the ghee is $10$kg.

Thus, the option (A) is the correct option.

Note:
The strength of the vanaspati ghee is given as the ratio of the amount of vanaspati ghee with the total amount of ghee and after adding $10$kg of pure ghee the total amount of ghee becomes $\left( {x + 10} \right)$kg.