12 men or 30 boys can complete a work in 72 days. How many days will 48 men and 24 boys will take to complete the same work?

Options

A. 20
B. 18
C. 15
D. 25

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Understand the Work Done
We know that 12 men or 30 boys can complete a work in 72 days. This means that the total work can be expressed in terms of either men or boys.

### Step 2: Calculate Total Work
Let's calculate the total work using boys:
- Total work (in boy-days) = Number of boys × Number of days
- Total work = 30 boys × 72 days = 2160 boy-days

### Step 3: Establish the Relationship Between Men and Boys
From the problem, we have:
- 12 men = 30 boys
This can be simplified to find the efficiency of men in terms of boys:
- 2 men = 5 boys
- Therefore, 1 man = 5/2 boys

### Step 4: Convert Men to Boys
Now, let's convert 48 men into an equivalent number of boys:
- 48 men = 48 × (5/2) boys = 120 boys

### Step 5: Calculate the Total Number of Boys
Now, we add the number of boys:
- Total boys = 120 boys (from men) + 24 boys = 144 boys

### Step 6: Calculate the Time Taken by 144 Boys
Now we need to find out how many days 144 boys will take to complete the same work:
- Time = Total work / Number of workers
- Time = 2160 boy-days / 144 boys = 15 days

### Final Answer
Thus, 48 men and 24 boys will take **15 days** to complete the same work.

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