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A and B can do a piece of work in 30 days and 45 days respectively. They start working together. After working three days A leaves and another person C joins to B. If B and C both finish the rest of work in 25/2 days then in how many days C can finish the work alone?
- a)71/3 days
- b)45/2 days
- c)45 days
- d)25 days
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Given: A can do the work in 30 days.
B can do the work in 45 days.
A and B work together for 3 days.
B and C complete the remaining work in 25/2 days.
Let's assume the total work to be done is 90 units (LCM of 30 and 45).
So, A can do 3 units of work in a day (90/30)
And, B can do 2 units of work in a day (90/45)
After working together for 3 days, the work done by A and B will be:
A = 3 * 3 = 9 units
B = 2 * 3 = 6 units
Total work done = 15 units
Remaining work = 90 - 15 = 75 units
Let's assume C can do x units of work in a day.
So, B and C together can do (2 + x) units of work in a day.
We know that B and C complete the remaining work in 25/2 days.
So, (2 + x) * (25/2) = 75
2 + x = 15/2
x = 11/2
Therefore, C can do 11/2 units of work in a day.
To complete the entire work alone, C will take:
90 / (2 + 11/2) = 45/2 days
Hence, the answer is option B.
B can do the work in 45 days.
A and B work together for 3 days.
B and C complete the remaining work in 25/2 days.
Let's assume the total work to be done is 90 units (LCM of 30 and 45).
So, A can do 3 units of work in a day (90/30)
And, B can do 2 units of work in a day (90/45)
After working together for 3 days, the work done by A and B will be:
A = 3 * 3 = 9 units
B = 2 * 3 = 6 units
Total work done = 15 units
Remaining work = 90 - 15 = 75 units
Let's assume C can do x units of work in a day.
So, B and C together can do (2 + x) units of work in a day.
We know that B and C complete the remaining work in 25/2 days.
So, (2 + x) * (25/2) = 75
2 + x = 15/2
x = 11/2
Therefore, C can do 11/2 units of work in a day.
To complete the entire work alone, C will take:
90 / (2 + 11/2) = 45/2 days
Hence, the answer is option B.
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