Suman can do a work in 3 days. Sumat can do the same work in 2 days. Both of them finish the work together and get Rs 150. What is the share of Suman ?

Options

A. Rs 30
B. Rs 60
C. Rs 70
D. Rs 75

Answer

To solve the problem step by step, we will calculate the share of Suman based on the work done by both Suman and Sumit.

### Step 1: Determine the work rates of Suman and Sumit.
- Suman can complete the work in 3 days. Therefore, Suman's work rate is:
\[ \text{Work rate of Suman} = \frac{1}{3} \text{ (work per day)} \]
- Sumit can complete the work in 2 days. Therefore, Sumit's work rate is:
\[ \text{Work rate of Sumit} = \frac{1}{2} \text{ (work per day)} \]

### Step 2: Calculate the combined work rate of Suman and Sumit.
- The combined work rate when both work together is:
\[ \text{Combined work rate} = \text{Work rate of Suman} + \text{Work rate of Sumit} = \frac{1}{3} + \frac{1}{2} \]
- To add these fractions, we need a common denominator. The least common multiple of 3 and 2 is 6. Thus:
\[ \frac{1}{3} = \frac{2}{6} \quad \text{and} \quad \frac{1}{2} = \frac{3}{6} \]
- Now, adding these:
\[ \text{Combined work rate} = \frac{2}{6} + \frac{3}{6} = \frac{5}{6} \text{ (work per day)} \]

### Step 3: Determine the ratio of their efficiencies.
- The efficiency of Suman and Sumit can be determined by the inverse of the time taken to complete the work:
- Suman's efficiency = 1/3 (work done per day)
- Sumit's efficiency = 1/2 (work done per day)
- The ratio of their efficiencies is the inverse of the time taken:
\[ \text{Efficiency ratio} = \text{Sumit : Suman} = 2 : 3 \]

### Step 4: Calculate the total parts based on their efficiencies.
- The total parts of the work done based on their efficiencies are:
\[ \text{Total parts} = 2 + 3 = 5 \text{ parts} \]

### Step 5: Calculate Suman's share of the total payment.
- The total payment for the work is Rs 150. Suman's share corresponds to 2 parts out of the total 5 parts:
\[ \text{Suman's share} = \frac{2}{5} \times 150 \]
- Calculating this:
\[ \text{Suman's share} = \frac{150 \times 2}{5} = \frac{300}{5} = 60 \]

### Conclusion:
- Therefore, Suman's share of the payment is Rs 60.