G is twice as fast as S in doing work .If G can do a work in 30 days less than S ,how many days will they take to complete the work together ?

A.25

B. 20

C. 22

D. 15

Options

A. D
B. B
C. A
D. C

Answer

To solve the problem, we need to determine how many days G and S will take to complete the work together, given that G is twice as fast as S and that G can complete the work in 30 days less than S.

### Step-by-Step Solution:

1. **Define Variables**:
- Let the number of days S takes to complete the work be \( x \).
- Since G is twice as fast as S, G will take \( \frac{x}{2} \) days to complete the same work.

2. **Set Up the Equation**:
- According to the problem, G takes 30 days less than S:
\[ \frac{x}{2} = x - 30 \]

3. **Solve the Equation**:
- Multiply both sides by 2 to eliminate the fraction:
\[ x = 2x - 60 \]
- Rearranging gives:
\[ 60 = 2x - x \]
\[ x = 60 \]

4. **Determine G's Days**:
- Since S takes 60 days, G takes:
\[ \frac{60}{2} = 30 \text{ days} \]

5. **Calculate Work Done Per Day**:
- Work done by S in one day:
\[ \text{Work by S} = \frac{1}{60} \text{ (units of work per day)} \]
- Work done by G in one day:
\[ \text{Work by G} = \frac{1}{30} \text{ (units of work per day)} \]

6. **Combine Their Work**:
- Together, the work done in one day by both G and S:
\[ \text{Total work per day} = \frac{1}{60} + \frac{1}{30} \]
- To add these fractions, find a common denominator (which is 60):
\[ \frac{1}{60} + \frac{2}{60} = \frac{3}{60} = \frac{1}{20} \]

7. **Calculate Total Days to Complete Work Together**:
- If they can do \( \frac{1}{20} \) of the work in one day, then the total number of days to complete the work together is:
\[ \text{Total days} = \frac{1}{\left(\frac{1}{20}\right)} = 20 \text{ days} \]

### Final Answer:
Thus, G and S will take **20 days** to complete the work together.