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Anil can do a piece of work in 14 days w...

Anil can do a piece of work in 14 days which Rohit can do in 21 days. They worked together for few days after which Anil Ieft. If Rohit worked alone for 3 days, find the total number of days he took to complete the whole work.
A. 31/5
B. 51/5
C. 21/5
D. 13/5

A

D

B

B

C

C

D

A

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we will follow these calculations: ### Step 1: Determine the work done by Anil and Rohit Anil can complete the work in 14 days, and Rohit can complete it in 21 days. To find their efficiencies, we can calculate the amount of work they can do in one day. - Total work can be considered as the least common multiple (LCM) of 14 and 21, which is 42 units. - Anil's efficiency = Total work / Time taken by Anil = 42 / 14 = 3 units per day. - Rohit's efficiency = Total work / Time taken by Rohit = 42 / 21 = 2 units per day. ### Step 2: Calculate combined efficiency When Anil and Rohit work together, their combined efficiency is: - Combined efficiency = Anil's efficiency + Rohit's efficiency = 3 + 2 = 5 units per day. ### Step 3: Set up the equation for the work done Let’s assume they worked together for \( X \) days. The work done by both of them together in \( X \) days is: - Work done together = Combined efficiency × Days worked = 5X units. After working together for \( X \) days, Anil leaves, and Rohit works alone for 3 days. The work done by Rohit in those 3 days is: - Work done by Rohit alone = Rohit's efficiency × Days worked = 2 × 3 = 6 units. ### Step 4: Write the equation for total work The total work done by both Anil and Rohit together and then by Rohit alone should equal the total work: \[ 5X + 6 = 42 \] ### Step 5: Solve for \( X \) Rearranging the equation: \[ 5X = 42 - 6 \] \[ 5X = 36 \] \[ X = \frac{36}{5} \] ### Step 6: Calculate total days taken Now, the total number of days taken to complete the work is the days they worked together plus the days Rohit worked alone: \[ \text{Total days} = X + 3 = \frac{36}{5} + 3 \] Convert 3 into a fraction: \[ 3 = \frac{15}{5} \] So, \[ \text{Total days} = \frac{36}{5} + \frac{15}{5} = \frac{51}{5} \] ### Conclusion The total number of days taken to complete the whole work is \( \frac{51}{5} \). ### Final Answer The correct option is B. \( \frac{51}{5} \).
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