Thirty men can do a piece of work in 16 days working 8 hours a day. How many men are needed to complete another work, which is twice the first one, in 10 days working 12 working a day?
The following are the steps involved in solving the above problem. Arrange them in sequential order.
`M_(2)=(30xx16xx8xx2x)/(x xx12xx10)`
`(30xx16xx8)/(x)=(M_(2)xx12xx10)/(2x)`
`(M_(1)D_(1)H_(1))/(W_(1))=(M_(2)D_(2)H_(2))/(W_(2))`
`M_(2)=64`

Options

A. CBAD
B. ACBD
C. ABCD
D. BACD

Explanation

To solve the problem step-by-step, we can follow the logical sequence of calculations based on the information given. Here’s how we can derive the solution:

### Step 1: Understand the Given Information
We know that:
- 30 men can complete a piece of work in 16 days working 8 hours a day.
- We need to find out how many men (M2) are needed to complete another work, which is twice the first one (W2 = 2 * W1), in 10 days working 12 hours a day.

### Step 2: Calculate the Total Work Done in the First Scenario
The total work (W1) can be calculated as:
\[ W_1 = \text{Number of men} \times \text{Number of days} \times \text{Number of hours per day} \]
\[ W_1 = 30 \text{ men} \times 16 \text{ days} \times 8 \text{ hours/day} \]
\[ W_1 = 3840 \text{ man-hours} \]

### Step 3: Calculate the Total Work for the Second Scenario
Since the second work is twice the first work:
\[ W_2 = 2 \times W_1 = 2 \times 3840 = 7680 \text{ man-hours} \]

### Step 4: Set Up the Equation Using the Work Formula
Using the formula for work:
\[ \frac{M_1 \times D_1 \times H_1}{W_1} = \frac{M_2 \times D_2 \times H_2}{W_2} \]
Substituting the known values:
\[ \frac{30 \times 16 \times 8}{3840} = \frac{M_2 \times 10 \times 12}{7680} \]

### Step 5: Simplify the Left Side
The left side simplifies to:
\[ \frac{30 \times 16 \times 8}{3840} = 1 \]
So the equation becomes:
\[ 1 = \frac{M_2 \times 10 \times 12}{7680} \]

### Step 6: Solve for M2
Now, cross-multiply to solve for M2:
\[ M_2 \times 10 \times 12 = 7680 \]
\[ M_2 \times 120 = 7680 \]
\[ M_2 = \frac{7680}{120} \]
\[ M_2 = 64 \]

### Final Answer
Thus, the number of men needed to complete the second work is **64 men**.

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