Question

The fifth part of a number when increased by 5 equals its fourth part decreased by 5. Find the number

Answer 1

Hint: Assume that the number is x. Hence find the expression for the fifth part of the number increased by 5 and the expression for the fourth part of the number decreased by 5. Equate the expressions and hence form an equation in x. Solve for x. Hence find the value of the number. Verify your answer.

Complete step-by-step answer:
Let the number be x.
Hence, we have the fifth part of the number $=\dfrac{x}{5}$
Hence, we have the fifth part of the number increased by 5 $=\dfrac{x}{5}+5$
Also, we have the fourth part of the number $=\dfrac{x}{4}$
Hence, we have the fourth part of the number decreased by 5$=\dfrac{x}{4}-5$
According to the question, we have the fifth part of the number increased by 5 equal to the fourth part of the number decreased by 5
Hence, we have
$\dfrac{x}{5}+5=\dfrac{x}{4}-5$
Adding 5 on both sides, we get
$\dfrac{x}{5}+10=\dfrac{x}{4}$
Subtracting $\dfrac{x}{5}$ from both sides, we get
$\dfrac{x}{4}-\dfrac{x}{5}=10$
Multiplying both sides, by 20 we get
$5x-4x=200$
Hence, we have x = 200
Hence the number is 200

Note: Verification:
The fifth part of 200 is equal to $\dfrac{200}{5}=40$
Hence the fifth part of 200 increased by equals 45
Also, the fourth part of 200 $=\dfrac{200}{4}=50$
Hence, the fourth part of 200 decreased by 5 equals 45
Hence the fifth part of 200 increased by 5 equal to the fourth part of 200 decreased by 5
Hence, our answer is verified to be correct.