Question

Rakesh went to a stationary shop to purchase a total of $38$ pens, erasers and sharpeners. He purchased at least $11$ items of each. He purchased more sharpeners than erasers and more erasers than pens. How many pens did he purchase?

• A. $11$
• B. $12$
• C. $13$
• D. $14$

Answer 1

The correct option is A $11$

Given that Rakesh purchased at least $11$ items of each

Let the number of pens, erasers, and sharpeners be $(11+p),(11+e),$ and $(11+s)$ respectively, such that-

(i) $s>e>p$ ........ (Given)

(ii) $s,e,p\in I^{+}$

Rakesh went to a stationary shop to purchase a total of $38$ pens, eraser, and sharpeners.

$\therefore (11+p)+(11+e)+(11+s)=38$

$\Rightarrow p+e+s+33=38$

$\Rightarrow p+e+s=5$

$0,2$ and $3$ and $0,1$ and $4$ are the only unequal positive integral values which results $5$ on addition.

$\because s>e>p$

$\therefore p=0,e=2or1,s=3or4$

Hence, no. of pens Rakesh purchased $=11+0=11$