Question: A, B and C together can do a work in 4 days. A and B alone can do it in 12 days and 10 days. How long will C can do it alone?
(a) 10 days
(b) 15 days
(c) 12 days
(d) 9 days
Ans: (b) 15 days
Explanation:
To solve the problem using the LCM method, let’s break it into steps:
Step 1: Calculate the total work
Let the total work be the LCM of the time taken by A, B, and C together and the time taken by A and B alone.
- A, B and C together: 4 days
- A alone: 12 days
- B alone: 10 days
Take the LCM of 4, 12, and 10, which is 60 units.
Thus, the total work is 60 units.
Step 2: Calculate the work done per day
A, B, and C’s Efficiency = \displaystyle \frac{60}{4} = 15 units/day
A’s Efficiency = \displaystyle \frac{60}{12} = 5 units/day
B’s Efficiency = \displaystyle \frac{60}{10} = 6 units/day
Step 3: Find C’s work per day
C’s Efficiency = Work done by (A, B, and C together) − Work done by (A and B together)
\qquad \qquad \quad= 15 – (5 + 6)
\qquad \qquad \quad= 15 – 11
\qquad \qquad \quad= 4 units/day
Step 4: Calculate the time taken by C to complete the work alone
Since C does 4 units/day, the time taken by C to complete 60 units is:
Time = \displaystyle \frac{\text{Total Work}}{\text{C's Work/Day}} =\displaystyle \frac{60}{4} = 15 days
Final Answer:
(b) 15 days
Similar Problem
- A, B and C together can do a piece of work in 8 days. If B alone can do the work in 18 days and C alone can do the same work in 24 days, in how many days A alone can finish the work? [Ans: 36 days]
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