A number is 124 more than its one-third. What is that number?

A number is 124 more than its one-third. What is that number?

194
180
189
186
This question was previously asked in
UPSC CAPF – 2022
Let the number be $x$.
The problem states that “a number is 124 more than its one-third”.
This can be written as an equation:
$x = 124 + \frac{1}{3}x$

To solve for $x$, first move the term with $x$ to one side:
$x – \frac{1}{3}x = 124$

Combine the $x$ terms:
$\left(1 – \frac{1}{3}\right)x = 124$
$\left(\frac{3}{3} – \frac{1}{3}\right)x = 124$
$\frac{2}{3}x = 124$

Multiply both sides by $\frac{3}{2}$ to isolate $x$:
$x = 124 \times \frac{3}{2}$
$x = (124/2) \times 3$
$x = 62 \times 3$
$x = 186$

The number is 186.

– Translating a word problem into a mathematical equation.
– Solving a linear equation involving fractions.
To verify the answer, check if 186 is 124 more than its one-third:
One-third of 186 is $186 / 3 = 62$.
124 more than 62 is $124 + 62 = 186$.
The condition is satisfied, so the answer is correct.