Question

X can do a work in 10 days. X and Y both together can do the same work in 6 days. Then Y alone can do the work in

• A. 14 days
• B. 15 days
• C. 16 days
• D. 18 days

Hint:

Work rates add when people work together; use reciprocal of time to find rates and calculate unknowns.

Answer 1

The Correct Option is B

Step 1: Define work rates
X's work rate = \(\frac{1}{10}\) work/day (since X completes work in 10 days).
X and Y's combined work rate = \(\frac{1}{6}\) work/day.
Step 2: Find Y's work rate
Y's work rate = (X and Y's rate) - X's rate \[ = \frac{1}{6} - \frac{1}{10} = \frac{5 - 3}{30} = \frac{2}{30} = \frac{1}{15}. \]
Step 3: Find time taken by Y alone
Y alone can do the work in \(\frac{1}{\text{Y's rate}} = 15\) days.
Step 4: Conclusion
Y alone can do the work in 15 days.