A, B and C do a piece of work in, 8,16 and 24 days, respectively. They work together and earn Rs. 528. What is the share of B?

Options

A. Rs. 144
B. Rs. 152
C. Rs. 176
D. Rs. 168

Explanation

To solve the problem, we need to determine the share of B when A, B, and C work together. Here’s a step-by-step breakdown of the solution:

### Step 1: Calculate the work done by A, B, and C in one day.

- A can complete the work in 8 days, so the work done by A in one day is:
\[ \text{Work done by A in one day} = \frac{1}{8} \]

- B can complete the work in 16 days, so the work done by B in one day is:
\[ \text{Work done by B in one day} = \frac{1}{16} \]

- C can complete the work in 24 days, so the work done by C in one day is:
\[ \text{Work done by C in one day} = \frac{1}{24} \]

### Step 2: Calculate the total work done by A, B, and C together in one day.

To find the total work done by A, B, and C together in one day, we add their individual contributions:
\[ \text{Total work in one day} = \frac{1}{8} + \frac{1}{16} + \frac{1}{24} \]

To add these fractions, we need a common denominator. The least common multiple (LCM) of 8, 16, and 24 is 48.

Now, converting each fraction:
\[ \frac{1}{8} = \frac{6}{48}, \quad \frac{1}{16} = \frac{3}{48}, \quad \frac{1}{24} = \frac{2}{48} \]

Adding them together:
\[ \text{Total work in one day} = \frac{6}{48} + \frac{3}{48} + \frac{2}{48} = \frac{11}{48} \]

### Step 3: Calculate the share of B based on the work done.

The share of each person is proportional to the amount of work they do. B's share of the total work done in one day is:
\[ \text{B's work} = \frac{1}{16} \]

Now, we find the ratio of B's work to the total work done by A, B, and C together:
\[ \text{Ratio of B's work} = \frac{\frac{1}{16}}{\frac{11}{48}} = \frac{48}{16 \times 11} = \frac{3}{11} \]

### Step 4: Calculate B's share of the total earnings.

The total earnings for the work done is Rs. 528. B's share of the earnings can be calculated as follows:
\[ \text{B's share} = \text{Total earnings} \times \text{Ratio of B's work} = 528 \times \frac{3}{11} \]

Calculating B's share:
\[ \text{B's share} = 528 \div 11 \times 3 = 48 \times 3 = 144 \]

### Final Answer:
B's share of the earnings is Rs. 144.

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