Question

One-third of a number when decreased by 2 equals to one-fifth of the increased by 8.find the number.

Answer 1

let the number be x
1/3of x-2=1/5 of x +8
x/3-2=x/5+8
x/3-x/5=10
5x-3x/15=10 [lcm of 3 and 5=15]
2x=150
x=75
hence the number is 75

Answer 2

The required number is 17.

Let the number be 'n'.

When this no. is decreased by 2, it becomes = (n-2)

And one-third of this resulted no. equals to = (1/3) × (n-2) = $\frac{(n-2)}{3}$       ...(1)

Again, when the no. 'n' is increased by 8, it becomes = (n+8)

And one-fifth of this resulted no. equals to = (1/5) × (n+8) = $\frac{(n+8)}{5}$         ...(2)

It is given in the question that (1) and (2) are equal.

So, $\frac{(n-2)}{3}$ = $\frac{(n+8)}{5}$

Cross multiplying, we get

3(n+8) = 5(n-2)

⇒ 3n + 24 = 5n - 10

⇒5n -3n = 24 + 10

⇒ 2n = 34

⇒ n = 34/2 = 17

So, the required no. is 17.