A's 2 days' work is equal to B's 3 days' work. If A can complete the work in 8 days then to complete the work B will take

Options

A. 14 days
B. 12 days
C. 15 days
D. 16 days

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Work Ratio
We know from the problem that A's 2 days' work is equal to B's 3 days' work. This can be expressed mathematically as:
\[ 2 \text{ (A's work in 2 days)} = 3 \text{ (B's work in 3 days)} \]
From this, we can derive the efficiency (work done per day) of A and B.

### Step 2: Calculate A's Efficiency
If A can complete the work in 8 days, then A's efficiency can be calculated as:
\[ \text{Efficiency of A} = \frac{1 \text{ (total work)}}{8 \text{ (days)}} = \frac{1}{8} \text{ (work per day)} \]

### Step 3: Relate A's and B's Efficiency
From the ratio of their work, we have:
\[ \frac{\text{Efficiency of A}}{\text{Efficiency of B}} = \frac{3}{2} \]
Let the efficiency of B be \( b \). Then:
\[ \frac{\frac{1}{8}}{b} = \frac{3}{2} \]

### Step 4: Solve for B's Efficiency
Cross-multiplying gives:
\[ 1 \cdot 2 = 3 \cdot 8b \]
\[ 2 = 24b \]
\[ b = \frac{2}{24} = \frac{1}{12} \text{ (work per day)} \]

### Step 5: Calculate Time Taken by B
Now that we have B's efficiency, we can find out how long it will take for B to complete the entire work:
\[ \text{Time taken by B} = \frac{1 \text{ (total work)}}{\text{Efficiency of B}} = \frac{1}{\frac{1}{12}} = 12 \text{ days} \]

### Final Answer
Thus, B will take **12 days** to complete the work.

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