A can do a work in 10 days, B can do the same work in 20 days. After working for 4 days B left the job & C started working at the place of B, the remaining work was done by both A & C in 2 days. In how many days C alone can do the work?
Step-by-step Solution:
Note: The problem statement "After working for 4 days B left" is slightly ambiguous. The interpretation that leads to the correct answer is that A and B worked together for 4 days before B left.
1. Define Individual Rates (per day) - Rate of A = 1/10 of the work.
- Rate of B = 1/20 of the work.
2. Find Work Done by A and B in 4 Days - Combined rate of (A+B) = 1/10 + 1/20 = (2+1)/20 = 3/20 per day.
- In 4 days, the work they complete together is: (3/20) × 4 = 12/20 = 3/5 of the work.
3. Find the Remaining Work - The remaining part of the work is 1 - 3/5 = 2/5.
4. Find the Rate of C - We are told that A and C finish the remaining 2/5 of the work in 2 days.
- This means their combined rate (A+C) is: Work ÷ Time = (2/5) ÷ 2 = 1/5 per day.
- To find C's rate, we subtract A's rate: Rate(C) = Rate(A+C) - Rate(A) = 1/5 - 1/10 = 1/10.
5. Calculate Time for C Alone - If C's rate is 1/10 of the work per day, the time C takes to complete the entire job alone is the reciprocal of its rate.
- Time = 1 / (1/10) = 10 days.
Final Answer: C alone can do the work in 10 Days.