JAMB 2023 Mathematics · Question 11

It takes 12 men 8 hours a day to finish a piece of work in 4 days. In how many days will it take 4 men working…

Question

It takes 12 men 8 hours a day to finish a piece of work in 4 days. In how many days will it take 4 men working 16 hours a day to complete the same piece of work?

A.6 days
B.8 days
C.10 days
D.12 days

Answer: A. 6 days

Explanation written with AI and checked against the answer key

Analysis

This is a classic "Work-Rate" problem. The total amount of work remains constant, so we can use the principle that the product of the number of workers, the time spent per day, and the number of days is equal to the total work done.

Concept

The formula for work-related problems is:

\frac{M_1 \times T_1 \times D_1}{W_1} = \frac{M_2 \times T_2 \times D_2}{W_2}

Where:

M = Number of men
T = Time (hours per day)
D = Number of days
W = Total work (since the work is the same in both cases, $W_1 = W_2$ , so they cancel out).

Step-by-Step Solution

Step 1: Identify the given values.

$M_1 = 12$ men
$T_1 = 8$ hours/day
$D_1 = 4$ days
$M_2 = 4$ men
$T_2 = 16$ hours/day
$D_2 = ?$ (This is what we need to find)

Step 2: Set up the equation.

12 \times 8 \times 4 = 4 \times 16 \times D_2

Step 3: Calculate the left side.

12 \times 8 = 96

96 \times 4 = 384

Step 4: Calculate the right side.

4 \times 16 = 64

384 = 64 \times D_2

Step 5: Solve for $D_2$ .

D_2 = \frac{384}{64}

D_2 = 6

It will take 4 men working 16 hours a day exactly 6 days to complete the work.

Exam Tip

When solving these problems, always remember that the number of men and the number of days are inversely proportional. If you reduce the number of men, the number of days must increase (assuming hours remain constant). If you increase the hours worked per day, the number of days must decrease. Checking this logic helps you avoid simple calculation errors!

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