Question

When 105 is added to one third of a number, the result is two times the original number. What is the original number?

Answer 1

Let the number be x.

One third of the number = x/3.

Number added to x/3 = 105.

Twice the original number = 2x.

According to condition,

x + (x/3+105) = 2x

or, x + {(x+315)/3} = 2x

or, x + (x+315)/3 = 2x

or, (3x+x+315)/3 = 2x

or, 4x + 315 = 2x × 3

or, 4x + 315 = 6x

or, 6x = 4x + 315

or, 6x - 4x = 315

or, 2x = 315

or, x = 315/2

or, x = 157 ¹/₂

or, x = 157.5

Hence, the original number is 157.5.

Hope this helps you to get to your answer.