Question

A number whose fifth part increased by 5 is equal to its fourth part diminished by 5.Find the number.

Answer 1

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Let a number be x.

Fifth part of the number = x/5

Fifth part of the number increased by 5 = x/5 + 5

Fourth part of the number = x/4

Fourth part of the number diminished by 5 = x/4 - 5

⇒ x/5 + 5 = x/4 - 5

⇒ x/5 - x/4  = - 5 - 5

⇒ x/5 - x/4  = - 5 - 5

⇒ -x/20 = -10

⇒ x = 200

Therefore, the required number is 200.

Answer 2

Let fifth part = x/5

Fourth part = x/4

According to given condition

x/5+5 = x/4-5

(x+25)/5 = (x-20)/4

4x+100 = 5x -100

100+100=5x-4x

200=x

x = 200