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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 ?

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Last updated date: 22nd Jun 2024
Total views: 414k
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Answer
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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.


Complete step-by-step answer:
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 $x$.