The sum of a number and one-third of itself is 24. Find the number.

Class 8Linear Equations in One VariableLinear Equations

Step-by-Step Solution

Let the number be

x . x + \frac{x}{3} = 24

→ multiply by 3:

3 x + x = 72

→

4 x = 72

→

x = 18

Answer: D) 18

Multiplying both sides by the LCM of denominators turns fractions into whole numbers in one move.

Example:

\frac{x}{2} + \frac{1}{3} = \frac{5}{6}

. LCM of 2, 3, 6 = 6. Multiply every term by 6:

6 \times \frac{x}{2} + 6 \times \frac{1}{3} = 6 \times \frac{5}{6} 3 x + 2 = 53 x = 3, x = 1

.

Verify:

\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}

. ✓

Don't just memorise the answer — build a daily practice habit.