If 90 men can do a certain job in 16 days, working 12 hours day, then the part of that work which can be completed by 70 men in 24 days wokring 8 hours/day is.

Options

A. 1. `(5)/(8)`
B. 2. `(1)/(3)`
C. 3. `(7)/(9)`
D. 4. `(2)/(3)`

Answer

To solve the problem step by step, we will use the concept of work done, which can be calculated using the formula:

\[ \text{Work} = \text{Number of Men} \times \text{Number of Days} \times \text{Number of Hours per Day} \]

### Step 1: Calculate the total work done by 90 men in 16 days working 12 hours a day.

Using the formula:

\[ W_1 = M_1 \times D_1 \times H_1 \]

Where:
- \( M_1 = 90 \) (men)
- \( D_1 = 16 \) (days)
- \( H_1 = 12 \) (hours/day)

Substituting the values:

\[ W_1 = 90 \times 16 \times 12 \]

Calculating:

\[ W_1 = 90 \times 16 = 1440 \]
\[ W_1 = 1440 \times 12 = 17280 \text{ man-hours} \]

### Step 2: Calculate the total work done by 70 men in 24 days working 8 hours a day.

Using the same formula:

\[ W_2 = M_2 \times D_2 \times H_2 \]

Where:
- \( M_2 = 70 \) (men)
- \( D_2 = 24 \) (days)
- \( H_2 = 8 \) (hours/day)

Substituting the values:

\[ W_2 = 70 \times 24 \times 8 \]

Calculating:

\[ W_2 = 70 \times 24 = 1680 \]
\[ W_2 = 1680 \times 8 = 13440 \text{ man-hours} \]

### Step 3: Calculate the part of work completed by 70 men in 24 days working 8 hours a day compared to the total work done by 90 men in 16 days.

To find the part of the work completed by the second group of men compared to the total work done by the first group, we can take the ratio:

\[ \text{Part of work} = \frac{W_2}{W_1} \]

Substituting the values we calculated:

\[ \text{Part of work} = \frac{13440}{17280} \]

Simplifying the fraction:

\[ \text{Part of work} = \frac{13440 \div 13440}{17280 \div 13440} = \frac{1}{1.2857} \approx \frac{7}{9} \]

### Final Answer:
The part of the work which can be completed by 70 men in 24 days working 8 hours a day is \( \frac{7}{9} \) of the total work.

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