Solution
1. Assume the time taken:
Let the time taken by the woman to complete the full work be x hours.
Since the child is 15 hours slower, the time taken by the child to complete the full work is (x+15) hours.
2. Formulate the Work Equation:
According to the question, the child works for 18 hours and the woman works for 6 hours to complete 53 of the work:
3. Solve for x:
Divide the entire equation by 3 to simplify:
Factorizing the quadratic equation:
Since time cannot be negative, x=30.
So, the woman takes 30 hours to complete the entire job alone.
4. Calculate Remaining Time:
The question asks how much more time the woman needs to complete the remaining job now.
Work already completed = 53
Remaining work = 1−53=52
Time taken by woman for 52 work = 52×Total time taken by woman
Conclusion:
To complete the remaining job, the woman will take 12 hours.
Correct Option: (c) 12 hours
