Question

Ram bought 40 pens and 50 pencils at the cost of ₹350 and 30 pens and 40 pencils at the cost of ₹270. The cost of one pen and three pencils is:

[1 mark]

• A. ₹14
• B. ₹15
• C. ₹16
• D. ₹17

Answer 1

The correct option is A ₹14

Let the cost of a pen$=x$
Cost of a pencil $=y$
It is given that,
$40x+50y=\mathrm{350...}\left(1\right)$
$30x+40y=\mathrm{270...}\left(2\right)$

By multiplying (1) with 4 and (2) with 5,
We get, $160x+200y=\mathrm{1400...}\left(3\right)$
$150x+200y=\mathrm{135.....}\left(4\right)$

Subtracting (4) from (3), we get,
$10x=50$
$\Rightarrow x=₹5$
$\therefore \text{Cost of a pen}=₹5$

Substituting x in (1),
$40\left(5\right)+50y=350$
$y=\frac{150}{5}=3$
$\therefore \text{Cost of a pencil}=₹3$

$\text{Cost of one pen + three pencils}=x+3y=5+3\left(3\right)=₹14$