Question

If one-fourth of a number exceeds 20% of the number by 10, then the number is

• A. 150
• B. 180
• C. 200
• D. 250

Hint:

Convert percentages into fractions before forming equations.

Answer 1

The Correct Option is C

Let's solve the problem step-by-step:

We are given that one-fourth of a number exceeds 20% of that number by 10.

Let the number be \(x\).

One-fourth of the number is \(\frac{x}{4}\).

20% of the number is \(0.2 \cdot x\) or \(\frac{x}{5}\).

According to the problem, one-fourth of the number exceeds 20% of the number by 10. Therefore, we can write the equation:

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

To solve for \(x\), first eliminate the fractions by finding a common multiple of 4 and 5, which is 20:

Multiply the entire equation by 20:

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

This simplifies to:

\(5x = 4x + 200\)

Subtract \(4x\) from both sides of the equation:

\(5x - 4x = 200\)

This simplifies to:

\(x = 200\)

Thus, the number is 200.

Therefore, the correct answer is 200.