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. If each pen cost Rs. $2$ each eraser cost Rs. $3$ and each sharpener cost Rs. $4$. find the minimum expenditure be could have incurred on the items (in Rs.)

• A. $116$
• B. $118$
• C. $117$
• D. $119$

Answer 1

The correct option is C $117$

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 $3$ are the only unequal positive integral values which results $5$ on addition.

$\because s>e>p$

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

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

no. of erasers Rakesh purchased $=11+2=13$

no. of sharpners Rakesh purchased $=11+3=14$

Given that If each pen cost Rs. $2$ each eraser cost Rs. $3$ and each sharpener cost Rs. $4$.

$\therefore \text{total expenditure}=11\times 2+13\times 3+14\times 4=22+39+56=Rs.117$

The minimum expenditure be could have incurred on the items $=$ Rs. $117$