The working capacity of A is 50% more than that of B. If A can complete a work in 12 days, then in how many days B will complete this work?

Options

A. 18 days
B. 20 days
C. 15 days
D. 12 days

Answer

To solve the problem step by step, we need to determine how many days B will take to complete the same work that A can complete in 12 days, given that A's working capacity is 50% more than B's.

### Step 1: Understand the working capacities
Let the work rate of B be represented as \( R_B \). Since A's working capacity is 50% more than B's, we can express A's work rate as:
\[ R_A = R_B + 0.5 R_B = 1.5 R_B \]

### Step 2: Calculate A's work rate
Since A can complete the work in 12 days, we can express A's work rate in terms of the total work \( W \):
\[ R_A = \frac{W}{12} \]

### Step 3: Set up the equation
From Step 1, we know:
\[ R_A = 1.5 R_B \]
Substituting \( R_A \) from Step 2 into this equation gives us:
\[ \frac{W}{12} = 1.5 R_B \]

### Step 4: Solve for B's work rate
Rearranging the equation to find \( R_B \):
\[ R_B = \frac{W}{12 \times 1.5} = \frac{W}{18} \]

### Step 5: Calculate the time taken by B
Now that we have B's work rate, we can find out how long it will take B to complete the work \( W \):
\[ \text{Time taken by B} = \frac{W}{R_B} = \frac{W}{\frac{W}{18}} = 18 \text{ days} \]

### Final Answer
B will complete the work in **18 days**.

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