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.

Question

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.

Philoid · Accepted Answer

Let the number of pens be ‘a’ and number of pencils be ‘b’.

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.

⇒ a + b = 40 ------ (1)

Also, b + 5 = 4(a – 5)

⇒ b = 4a – 25 ------- (2)

Subtracting eq2 from eq1

⇒ a + b – b = 40 – 4a + 25

⇒ 5a = 65

⇒ a = 13