The time taken to do a piece of work is inversely proportional to the number of men employed. If it takes 45 men to do a piece of work 5 days, how long will it take 25 men?
Take Free Practice Test On 2026 JAMB UTME, Post UTME, WAEC SSCE, GCE, NECO SSCE
Correct Answer: Option D
Explanation:
If the time taken to do a piece of work is inversely proportional to the number of men employed, we can use the formula:
\[
T_1 \times M_1 = T_2 \times M_2
\]
Where:
- \(T_1\) is the time taken by the first group of men,
- \(M_1\) is the number of men in the first group,
- \(T_2\) is the time taken by the second group of men,
- \(M_2\) is the number of men in the second group.
Given:
- \(T_1 = 5\) days,
- \(M_1 = 45\) men,
- \(M_2 = 25\) men.
We need to find \(T_2\).
Using the formula:
\[
5 \times 45 = T_2 \times 25
\]
\[
225 = 25 \times T_2
\]
Solve for \(T_2\):
\[
T_2 = \frac{225}{25} = 9 \text{ days}
\]
If the time taken to do a piece of work is inversely proportional to the number of men employed, we can use the formula:
\[
T_1 \times M_1 = T_2 \times M_2
\]
Where:
- \(T_1\) is the time taken by the first group of men,
- \(M_1\) is the number of men in the first group,
- \(T_2\) is the time taken by the second group of men,
- \(M_2\) is the number of men in the second group.
Given:
- \(T_1 = 5\) days,
- \(M_1 = 45\) men,
- \(M_2 = 25\) men.
We need to find \(T_2\).
Using the formula:
\[
5 \times 45 = T_2 \times 25
\]
\[
225 = 25 \times T_2
\]
Solve for \(T_2\):
\[
T_2 = \frac{225}{25} = 9 \text{ days}
\]