A alone can do a piece of work in 12 days and B alone in 16 days. They under took to do the work for Rs 350. How much will B get ?

Options

A. Rs 150
B. Rs 200
C. Rs 250
D. Rs 180

Answer

To solve the problem of how much B will get from the total payment of Rs 350 for the work done together with A, we can follow these steps:

### Step-by-Step Solution:

1. **Determine A's Work Rate:**
- A can complete the work in 12 days.
- Therefore, A's work rate is \( \frac{1}{12} \) of the work per day.

2. **Determine B's Work Rate:**
- B can complete the work in 16 days.
- Therefore, B's work rate is \( \frac{1}{16} \) of the work per day.

3. **Find the LCM of A's and B's Days:**
- The LCM of 12 and 16 is 48. This will help us find the total work in terms of units.

4. **Calculate Work Done by A and B in One Day:**
- In 48 units of work:
- A's one day work: \( \frac{48}{12} = 4 \) units.
- B's one day work: \( \frac{48}{16} = 3 \) units.

5. **Calculate Total Work Done Together in One Day:**
- Together, A and B can do \( 4 + 3 = 7 \) units of work in one day.

6. **Calculate Total Days to Complete the Work:**
- Total work is 48 units.
- Days to complete the work together: \( \frac{48}{7} \) days.

7. **Calculate the Work Done by B:**
- In \( \frac{48}{7} \) days, B will do:
- Work done by B = \( 3 \) units/day \( \times \frac{48}{7} \) days = \( \frac{144}{7} \) units.

8. **Calculate the Share of B in Money:**
- Total payment for the work is Rs 350.
- B's share of the payment is proportional to the work done:
- B's share = \( \frac{\text{Work done by B}}{\text{Total work}} \times \text{Total payment} \)
- B's share = \( \frac{\frac{144}{7}}{48} \times 350 \)

9. **Simplify B's Share Calculation:**
- \( \frac{144}{7} \div 48 = \frac{144}{7 \times 48} = \frac{144}{336} = \frac{3}{7} \)
- So, B's share = \( \frac{3}{7} \times 350 = 150 \).

### Final Answer:
B will get Rs 150.

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