Reena has pens and pencils which together are 40 in number. If she has 5 more pencils and 5 less pens, then number of pencils would become 4 times the number of pens. Find the original number of pens and pencils.

Given:

Reena has pens and pencils which together are 40 in number. If she has 5 more pencils and 5 less pens, then number of pencils would become 4 times the number of pens. 

To do:

We have to find the original number of pens and pencils.

Let the number of pens and the number of pencils be $x$ and $y$ respectively.

According to the question,

$x + y = 40$.....(i)

$(y+5) =4(x-5) $

$y+5=4x-20$

$4x-y=5+20$

$4x-y=25$.....(ii)

Adding equations (i) and (ii), we get,

$x+y+4x-y=40+25$

$5x=65$

$x=\frac{65}{5}$

$x=13$

Substituting $x=13$ in equation (i), we get,

$13+y=40$

$y=40-13$

$y=27$

The original number of pens and pencils Reena had is 13 and 27 respectively.

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Updated on: 10-Oct-2022

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