A man and a woman working together can do a certain work in 22 hrs. If...
A man and a woman working together can do a certain work in 22 hrs. If...
Given:
- A man and a woman working together can do a certain work in 22 hrs.
- The skills of the man and woman are in the ratio 5:4.
Approach:
- Let the woman take x hours to finish the work.
- According to the given information, the man takes (22/5) hours to finish the work.
Calculation:
- Since the skills of the man and woman are in the ratio 5:4, the ratio of work done by them in 1 hour is 5:4.
- Let the total work be W. So, in 1 hour, the man completes (5/9)W work and the woman completes (4/9)W work.
- Therefore, the man completes the work in (22/5) hours, and the woman completes the work in x hours.
- Based on the above information, the equation can be formed as:
(5/9)W * (22/5) + (4/9)W * x = W
Solving the equation:
- Simplifying the equation, we get:
22 + 4x/9 = 1
4x/9 = 1 - 22
4x/9 = 1/9
4x = 1
x = 1/4
x = 4 hours
Conclusion:
- Therefore, the woman will take 4 hours to finish the work, which is equivalent to 49 ½ hours. Hence, the correct answer is option 'C'.