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# Ajinkya has twice as many pens with Sheetal and thrice as many pens with Heena. If they have in all 44 pens, how many pens does sheetal have ?

Last updated date: 22nd Jun 2024
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Hint: In these types of questions, we take a variable(generally say $x$) and other given conditions are also taken in the same variable. Finally, find the value of that variable according to the given relation by making an equation.

Ajinkya has twice as many pens with Sheetal. It means Sheetal has one-half pens as that of Ajinkya has. Let the number of pens Ajinkya has be $x$. Then, the number of pens Sheetal has $\dfrac{x}{2}$ . Also, Ajinkya has thrice as many pens with Heena. It means Heena has one-third pens as that of Ajinkya has. So, the number of pens Heena has $\dfrac{x}{3}$.
Given, all three have 44 pens.
Therefore, the sum of pens having all three is equal to 44.
$\therefore x + \dfrac{x}{2} + \dfrac{x}{3} = 44$
$\Rightarrow \dfrac{{6x + 3x + 2x}}{6} = 44$
$\Rightarrow \dfrac{{11x}}{6} = 44$
$\Rightarrow x = \dfrac{{44 \times 6}}{{11}}$
$\Rightarrow x = 24$
It means Ajinkya has $24$ pens.
The number of pens Sheetal has half as the number of pens of Ajinkya.
Therefore, number of of pens Sheetal has $= \dfrac{x}{2} = \dfrac{{24}}{2} = 12$

So, the correct answer is “Option A”.

Note:Check all the mathematical operations when solving the linear equation in one variable for finding the value of x and also remember that we have to find the value of $\dfrac{x}{2}$ here, not the value of $x$.