Kaushalya can do a work in 20 days, while Kaikeyi can do the same work in 25 days. They started the work jointly. Few days later Sumitra also joined them and thus all of them completed the whole work in 10 days. All of them were paid total Rs. 700. What is the share of Sumitra?

Options

A. Rs. 130
B. Rs. 185
C. Rs. 70
D. can't be determind

Answer

To solve the problem step by step, we will calculate the work done by each person and then determine Sumitra's share based on the total payment.

### Step 1: Determine the work rates of Kaushalya and Kaikeyi
- Kaushalya can complete the work in 20 days. Therefore, her work rate is:
\[ \text{Work rate of Kaushalya} = \frac{1 \text{ work}}{20 \text{ days}} = \frac{1}{20} \text{ work/day} \]
- Kaikeyi can complete the work in 25 days. Therefore, her work rate is:
\[ \text{Work rate of Kaikeyi} = \frac{1 \text{ work}}{25 \text{ days}} = \frac{1}{25} \text{ work/day} \]

### Step 2: Find the least common multiple (LCM) of their work durations
- The LCM of 20 and 25 is 100. We will consider the total work to be 100 units.

### Step 3: Calculate the daily work done by each person in terms of units
- Kaushalya's daily work in units:
\[ \text{Daily work of Kaushalya} = \frac{100 \text{ units}}{20 \text{ days}} = 5 \text{ units/day} \]
- Kaikeyi's daily work in units:
\[ \text{Daily work of Kaikeyi} = \frac{100 \text{ units}}{25 \text{ days}} = 4 \text{ units/day} \]

### Step 4: Calculate the total work done by Kaushalya and Kaikeyi in 10 days
- Total work done by Kaushalya in 10 days:
\[ \text{Work by Kaushalya} = 5 \text{ units/day} \times 10 \text{ days} = 50 \text{ units} \]
- Total work done by Kaikeyi in 10 days:
\[ \text{Work by Kaikeyi} = 4 \text{ units/day} \times 10 \text{ days} = 40 \text{ units} \]

### Step 5: Calculate the total work done by both and the remaining work
- Total work done by both:
\[ \text{Total work done by Kaushalya and Kaikeyi} = 50 + 40 = 90 \text{ units} \]
- Remaining work to be completed by Sumitra:
\[ \text{Remaining work} = 100 - 90 = 10 \text{ units} \]

### Step 6: Calculate the share of Sumitra based on the total payment
- The total payment for the work is Rs. 700. Since 100 units of work corresponds to Rs. 700, the value of 1 unit of work is:
\[ \text{Value of 1 unit} = \frac{700}{100} = 7 \text{ Rs/unit} \]
- Sumitra's share based on the 10 units of work she completed:
\[ \text{Share of Sumitra} = 10 \text{ units} \times 7 \text{ Rs/unit} = 70 \text{ Rs} \]

### Final Answer
Sumitra's share is Rs. 70.

---