Question

10 men and 6 women can do a piece of work in 4 days, whereas 12 men and 18 women can do it in 2 days. Find the ratio of the daily work done by a man to that done by a woman, respectively.

• A. 3 : 4
• B. 2 : 1
• C. 1 : 2
• D. 4 : 3

Answer 1

Answer:

A. 3 : 4

The ratio of the daily work done by a man to that done by a woman is 3:4.

Let the daily work capacity (efficiency) of one man be $M$ and one woman be $W$.

Step 1: Set up the total work equations
The total amount of work remains the same in both scenarios:

• Scenario 1: 10 men and 6 women working for 4 days
  $\text{Total Work} = (10M + 6W) \times 4$

• Scenario 2: 12 men and 18 women working for 2 days
  $\text{Total Work} = (12M + 18W) \times 2$

Step 2: Equate the two expressions
Since the total work is equal, we can set them equal to each other:
$(10M + 6W) \times 4 = (12M + 18W) \times 2$

Step 3: Simplify and solve for the ratio
Divide both sides by 2 to make calculations easier:
$2 \times (10M + 6W) = 12M + 18W$

Expand the brackets:
$20M + 12W = 12M + 18W$

Bring all $M$ terms to one side and $W$ terms to the other side:
$20M - 12M = 18W - 12W$
$8M = 6W$

Find the ratio of $M$ to $W$:
$\frac{M}{W} = \frac{6}{8}$

Simplify the fraction by dividing the numerator and denominator by 2:

$\frac{M}{W} = \frac{3}{4}$

The ratio of the daily work done by a man to that of a woman is 3:4.