18 men or 25 boys can complete a work in 25 days. How many days will 36 men and 10 boys take to complete the work?

Options

A. `(112)/(17)`
B. `(125)/(12)`
C. `(115)/(12)`
D. `(125)/(17)`

Answer

To solve the problem step by step, we will first determine the total work done in terms of "man-days" and then calculate how many days 36 men and 10 boys will take to complete the same work.

### Step 1: Calculate the total work done by 18 men and 25 boys in 25 days.

Given:
- 18 men can complete the work in 25 days.
- 25 boys can also complete the work in 25 days.

Let's calculate the work done by 18 men in man-days:
- Work done by 18 men in 25 days = 18 men × 25 days = 450 man-days.

Now, let's calculate the work done by 25 boys in man-days:
- Work done by 25 boys in 25 days = 25 boys × 25 days = 625 boy-days.

### Step 2: Convert the work done by boys into equivalent man-days.

To compare the work done by men and boys, we need to find the efficiency ratio of men to boys.
From the problem, we know that:
- 18 men = 25 boys.

Thus, the efficiency of 1 man compared to boys can be calculated as:
- 1 man = (25 boys / 18 men) = 25/18 boys.

### Step 3: Find the total work in terms of man-days.

Now, we can express the work done by boys in terms of men:
- 625 boy-days = 625 / (25/18) man-days = 625 × (18/25) man-days = 450 man-days.

Now we can conclude that the total work is equivalent to 450 man-days (from both men and boys).

### Step 4: Calculate the work capacity of 36 men and 10 boys.

Now, we need to find out how many days 36 men and 10 boys will take to complete the same work.

First, we calculate the total work capacity of 36 men and 10 boys in one day:
- Work done by 36 men in one day = 36 man-days.
- Work done by 10 boys in one day = 10 boys × (18/25) man-days (since 1 boy = 18/25 man-days) = 10 × (18/25) = 7.2 man-days.

Now, combine the two:
- Total work done by 36 men and 10 boys in one day = 36 + 7.2 = 43.2 man-days.

### Step 5: Calculate the number of days required to complete the work.

Now, we can find the number of days required to complete the total work of 450 man-days:
- Days required = Total work / Work done in one day = 450 man-days / 43.2 man-days per day.

Calculating this gives:
- Days required = 450 / 43.2 ≈ 10.42 days.

### Final Answer:
Therefore, 36 men and 10 boys will take approximately **10.42 days** to complete the work.

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