A is thrice as efficient as B.A and B cam complete a piece of work in 12 days. Find the number of days in which A alone complete it.

Options

A. 48
B. 16
C. 20
D. 32

Explanation

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

### Step 1: Understanding the Efficiency
Given that A is thrice as efficient as B, we can denote the efficiency of B as \( x \). Therefore, the efficiency of A will be \( 3x \).

### Step 2: Combine the Efficiencies
When A and B work together, their combined efficiency is:
\[ \text{Combined Efficiency} = \text{Efficiency of A} + \text{Efficiency of B} = 3x + x = 4x \]

### Step 3: Work Done in One Day
Since A and B together can complete the work in 12 days, we can find the total work in terms of efficiency:
\[ \text{Total Work} = \text{Combined Efficiency} \times \text{Number of Days} = 4x \times 12 = 48x \]

### Step 4: Finding the Days A Alone Will Take
Now, we need to find out how many days A alone will take to complete the same amount of work. The work done by A in one day is \( 3x \). Therefore, the number of days A will take to complete the total work is:
\[ \text{Days taken by A} = \frac{\text{Total Work}}{\text{Efficiency of A}} = \frac{48x}{3x} = 16 \text{ days} \]

### Final Answer
A alone will complete the work in **16 days**.

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