Question

I want to buy 40 articles consisting of pens at Rs. 4, erasers at Rs. 2 and rulers at Rs. 17. If I spend Rs. 301, how many of each do I buy?

• A. $13$, $14$, $13$ respectively
• B. $1$, $15$, $14$ respectively
• C. $10$, $10$, $20$ respectively
• D. $4$, $25$, $11$ respectively

Answer 1

The correct option is A $13$, $14$, $13$ respectively

Let number of pens$=p$

Number of erasers$=e$

Number of rulers$=r$

Total number of articles$=40$

$\therefore p+e+r=40\Rightarrow e=40-(p+r)$

Total cost$=301$

$4p+2e+17r=301$

$4p+80-2p-2r+17r=301$

$2p+15r=221\Rightarrow r=\left(\frac{221-2p}{15}\right)$

$2p<80(\because p<40)\therefore r\ge 9$ and off ($\because 2p$ is even )

If $r=11,p=\frac{(221-165)}{2}=28$

$\therefore e=40-(r+p)=1$

If $r=13,p=\frac{(221-195)}{2}=13$

$\therefore e=40-(p+r)=14$

$r=15,7p=-4$ (not possible)

$\therefore$Possible solutions are

$28$ pens, $1$ eraser and $11$ rulers

$13$ pens, $14$ erasers and $13$ rulers.