CAT 2020 Slot 2 QA Question 4: Aron bought some pencils and sharpeners. Spending the same amount of money as Aron, Aditya bought twice as many pencils and 10 less sharpeners. If the cost of one sharpener is ₹ 2 more than the cost o

Question

Aron bought some pencils and sharpeners. Spending the same amount of money as Aron, Aditya bought twice as many pencils and 10 less sharpeners. If the cost of one sharpener is ₹ 2 more than the cost o

Accepted Answer

Let Aron buy $p$ pencils and $s$ sharpeners. Let the cost of one pencil be ₹$x$. Then the cost of one sharpener is ₹$(x + 2)$.

The two amounts spent are equal.
$px + s(x+2) = 2px + (s-10)(x+2)$
$px = 10(x+2)$
$x(p-10) = 20$
$p = 10 + \dfrac{20}{x}$

Since $x$ is positive, $p$ must be greater than $

Aron bought some pencils and sharpeners. Spending the same amount of money as Aron, Aditya bought twice as many pencils and 10 less sharpeners. If the cost of one sharpener is ₹ 2 more than the cost of a pencil, then the minimum possible number of pencils bought by Aron and Aditya together is