A, B and C can do a work in x,3x and 5x days, respectively. They worked together and earned Rs. 460. What is the share of B?

Answer

To solve the problem, we need to determine the share of B in the total earnings of Rs. 460 based on the amount of work done by A, B, and C.

### Step 1: Determine the work done by A, B, and C
- A can complete the work in \( x \) days.
- B can complete the work in \( 3x \) days.
- C can complete the work in \( 5x \) days.

To find the work done by each in one day, we take the reciprocal of the number of days they take to complete the work:

- Work done by A in one day = \( \frac{1}{x} \)
- Work done by B in one day = \( \frac{1}{3x} \)
- Work done by C in one day = \( \frac{1}{5x} \)

### Step 2: Calculate the total work done by A, B, and C together in one day
The total work done by A, B, and C in one day is the sum of their individual work rates:

\[ \text{Total work done in one day} = \frac{1}{x} + \frac{1}{3x} + \frac{1}{5x} \]

To add these fractions, we need a common denominator. The least common multiple of \( x, 3x, \) and \( 5x \) is \( 15x \).

Rewriting each term with the common denominator:

\[ \frac{1}{x} = \frac{15}{15x}, \quad \frac{1}{3x} = \frac{5}{15x}, \quad \frac{1}{5x} = \frac{3}{15x} \]

Now, adding these fractions together:

\[ \text{Total work done in one day} = \frac{15 + 5 + 3}{15x} = \frac{23}{15x} \]

### Step 3: Calculate the total work done in terms of Rs.
Since they worked together and earned Rs. 460, we can determine how much work corresponds to this amount. The total work can be considered as 1 unit of work (the whole job).

### Step 4: Determine the share of B
To find B's share, we first need to find the ratio of work done by each person. The share of each person is proportional to the amount of work they contribute.

- Work done by A = \( \frac{1}{x} \)
- Work done by B = \( \frac{1}{3x} \)
- Work done by C = \( \frac{1}{5x} \)

The total work done by A, B, and C is \( \frac{23}{15x} \).

Now, we can calculate the share of B:

\[ \text{Share of B} = \frac{\text{Work done by B}}{\text{Total work done}} \times \text{Total earnings} \]

Substituting the values:

\[ \text{Share of B} = \frac{\frac{1}{3x}}{\frac{23}{15x}} \times 460 \]

Simplifying this:

\[ \text{Share of B} = \frac{1}{3} \times \frac{15}{23} \times 460 \]

Calculating:

\[ \text{Share of B} = \frac{15 \times 460}{3 \times 23} = \frac{6900}{69} = 100 \]

Thus, the share of B is Rs. 100.

### Final Answer:
The share of B is Rs. 100.