Ten boys or twenty girls can complete a job in 10 days. In how many days can a boy and a girl complete it

Options

A. 50
B. `58(1)/(3)`
C. `66(2)/(3)`
D. 70

Explanation

To solve the problem step by step, let's first understand the information given:

1. **Understanding the Work Rate**:
- 10 boys can complete a job in 10 days.
- 20 girls can also complete the same job in 10 days.
- This means that the work done by 10 boys in 10 days is equal to the work done by 20 girls in 10 days.

2. **Finding the Work Rate**:
- Work done by 10 boys in 10 days = 1 job
- Therefore, work done by 1 boy in 10 days = 1/10 job
- Hence, work done by 1 boy in 1 day = (1/10) / 10 = 1/100 job per day.

- Similarly, for girls:
- Work done by 20 girls in 10 days = 1 job
- Therefore, work done by 1 girl in 10 days = 1/20 job
- Hence, work done by 1 girl in 1 day = (1/20) / 10 = 1/200 job per day.

3. **Combining the Work Rates**:
- Now, we need to find out how much work is done by 1 boy and 1 girl together in one day.
- Work done by 1 boy in 1 day = 1/100 job
- Work done by 1 girl in 1 day = 1/200 job
- Therefore, work done by 1 boy and 1 girl in 1 day = (1/100 + 1/200).

4. **Finding a Common Denominator**:
- To add these fractions, we need a common denominator.
- The least common multiple of 100 and 200 is 200.
- Convert 1/100 to have a denominator of 200:
- 1/100 = 2/200.
- Now, we can add:
- (2/200 + 1/200) = 3/200.

5. **Calculating the Total Days**:
- If 1 boy and 1 girl together can complete 3/200 of the job in one day, then the total time taken to complete 1 job is the reciprocal of this rate:
- Total days = 1 / (3/200) = 200/3 days.

Thus, a boy and a girl together can complete the job in **200/3 days**, which is approximately **66.67 days**.