Question

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

Answer 1

Let the number of pens be x and that of pencil be y. then,

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

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

=> y + 5 = 4x - 20

=> 5 + 20 = 4x - y

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

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

x + 4x = 40 + 25

=> 5x = 65

${\displaystyle \Rightarrow x=\frac{65}{5}=13}$

Puttign x = 13 in equation (i) we get

13 + y = 40

=> y = 40 - 13 - 27

Hence, Reena has13 pens 27 pencils.