Question

A number whose fifth part increased by 4 is equal to its fourth part diminished by 10, is :

• A. 240
• B. 260
• C. 270
• D. 280

Answer 1

The Correct Option is D

Let the number be \( x \). 

According to the problem statement, the fifth part of the number when increased by 4 is equal to the fourth part diminished by 10.

Mathematically, this can be expressed as:

\(\frac{x}{5} + 4 = \frac{x}{4} - 10\)

To solve for \( x \), first eliminate the fractions by multiplying through by 20, the least common multiple of 5 and 4:

\(20 \left(\frac{x}{5} + 4\right) = 20 \left(\frac{x}{4} - 10\right)\)

This simplifies to:

\(4x + 80 = 5x - 200\)

Rearrange the equation to isolate \( x \):

\(4x + 80 - 5x = -200\)

\(-x + 80 = -200\)

Subtract 80 from both sides:

\(-x = -200 - 80\)

\(-x = -280\)

Multiply both sides by -1:

\(x = 280\)

Thus, the number is 280.