Twenty women together complete a piece of work in 16 days, 16 men together can complete the same work in 15 days. The ratio of the work ing capacity of a man to that of a woman is:

Options

A. `3:4`
B. `4:3`
C. `5:3`
D. `4:5`

Answer

To solve the problem, we need to determine the ratio of the working capacity of a man to that of a woman based on the information provided.

### Step 1: Calculate the total work done by women
We know that 20 women can complete the work in 16 days.
Let's denote the work done by one woman in one day as \( W_w \).

The total work \( W \) can be calculated as:
\[ W = \text{Number of women} \times \text{Days} \times \text{Work done by one woman in one day} \]
\[ W = 20 \times 16 \times W_w = 320 W_w \]

### Step 2: Calculate the total work done by men
Similarly, we know that 16 men can complete the same work in 15 days.
Let the work done by one man in one day be \( W_m \).

The total work \( W \) can also be calculated as:
\[ W = \text{Number of men} \times \text{Days} \times \text{Work done by one man in one day} \]
\[ W = 16 \times 15 \times W_m = 240 W_m \]

### Step 3: Set the total work equations equal to each other
Since both expressions represent the same total work \( W \), we can set them equal to each other:
\[ 320 W_w = 240 W_m \]

### Step 4: Solve for the ratio of \( W_m \) to \( W_w \)
Rearranging the equation gives us:
\[ \frac{W_m}{W_w} = \frac{320}{240} \]
Simplifying the fraction:
\[ \frac{W_m}{W_w} = \frac{32}{24} = \frac{4}{3} \]

### Step 5: Write the final ratio
Thus, the ratio of the working capacity of a man to that of a woman is:
\[ \text{Ratio of working capacity of a man to a woman} = 4:3 \]