Question

A positive integer $m$ is increased by 20% and the resulting number is 1080. Then the integer $m$ is

• A. 900
• B. 880
• C. 920
• D. 890

Hint:

Increase by $x\%$ means multiply original value by $(1 + \frac{x}{100})$.

Answer 1

The Correct Option is A

To solve the problem, we need to find the original integer \( m \) that, when increased by 20%, results in 1080.

1. First, express the relationship between the original number \( m \) and the increased number:

The increased number is 20% more than \( m \), which can be expressed as:

\(m + \frac{20}{100} \times m = 1080\)

1. Combine the terms on the left-hand side:

\(m + 0.2m = 1080\)

1. Simplify the expression:

\(1.2m = 1080\)

1. To find \( m \), divide both sides by 1.2:

\(m = \frac{1080}{1.2}\)

1. Calculate \( m \):

\(m = 900\)

Thus, the integer \( m \) is 900.

Explanation of Why 900 is Correct:

• If \( m = 900 \), when it is increased by 20%, it becomes:

\(900 + 0.2 \times 900 = 900 + 180 = 1080\)

• This confirms our calculation that an increase of 20% on 900 gives 1080, matching the given condition.