The sum of half, one-third and one-fifth of a number exceeds the number by 12. What is the number?

Correct option is C

Given:

The sum of half, one-third, and one-fifth of a number exceeds the number by 12.

Formula Used:

Let the number be x.

The equation for the problem is:

Half of the number + One-third of the number + One-fifth of the number = The number + 12.

Solution:

​$$\frac{x}{2} + \frac{x}{3} + \frac{x}{5} = x + 12\\\ \\\frac{15x}{30} + \frac{10x}{30} + \frac{6x}{30} = x + 12\\\ \\\frac{31x}{30} = x + 12$$​​

31x = 30(x + 12)

31x = 30x + 360

31x - 30x = 360

x = 360

Therefore, the number is 360.