Question

one third of a number increased by 5 is equal to its half part decreased by 5.fi nd the number

Answer 1

$\frac{x}{3} + 5 = \frac{x}{2} - 5 \\ 10 = \frac{x}{2} - \frac{x}{3} \\ 10 = \frac{3x - 2x}{6} \\ \frac{x}{6} = 10 \\ x = 60$
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Answer 2

Given: one third of a number increased by 5 is equal to its half part decreased by 5.

To find: The number.

Solution:

Let the number be equal to x. Now, one-third of the number can be written as follows.

$\frac{1}{3} * x = \frac{x}{3}$

Similarly, half of the number can be written as follows.

$\frac{1}{2} * x = \frac{x}{2}$

According to the question, the following equation is formed.

$\frac{x}{3} + 5 = \frac{x}{2} -5$

On rearranging, the value of x can be found since x is the only variable in the question and the rest are constants.

$\frac{x}{2} - \frac{x}{3} = 10$

$\frac{x}{6} = 10$

$x = 60$

Therefore, the number is 60.