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A and B start working on a project. After 10 days B is replaced by C who can complete the project alone in 20 days. If A and B together can complete the project in 30 days, then find the day on which the project will be completed after C replaces B, if the efficiency of B is twice that of A.
- a)15th day
- b)11th day
- c)9th day
- d)7th day
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A and B start working on a project. After 10 days B is replaced by C w...
Let the number of days required by B alone to complete the project be x
The number of days required by A alone to complete it = 2x
The number of days required by A alone to complete it = 2x
1/x + l/2x = 1/30
⇒ x = 45
⇒ x = 45
The part of work done in 10 days =1/3
Work done by A and C in 1 day = (1/90) + (1/20) = (11/180)
∴ The number of days taken by A and C = (2/3) / (11/180) = 120/11 = (10*12) / 11 days.
Work done by A and C in 1 day = (1/90) + (1/20) = (11/180)
∴ The number of days taken by A and C = (2/3) / (11/180) = 120/11 = (10*12) / 11 days.
Hence, option 2.
This question is part of UPSC exam. View all CAT courses
Most Upvoted Answer
A and B start working on a project. After 10 days B is replaced by C w...
Let's assume that the total work in the project is represented by 'W'.
Efficiency of A:
Let the efficiency of A be 'x'. So, A can complete 1/xth of the work in 1 day.
Efficiency of B:
Given that the efficiency of B is twice that of A. So, the efficiency of B is '2x'. Hence, B can complete 1/(2x)th of the work in 1 day.
Efficiency of A and B together:
When A and B work together, their combined efficiency is the sum of their individual efficiencies. Hence, their combined efficiency is 'x + 2x = 3x'. Therefore, A and B together can complete 1/(3x)th of the work in 1 day.
Efficiency of C:
Given that C can complete the project alone in 20 days. So, the efficiency of C is 1/20th of the total work per day.
Let's calculate the work done by A, B, and A+B in 10 days:
Work done by A in 10 days = (1/x) * 10 = 10/x
Work done by B in 10 days = (1/(2x)) * 10 = 10/(2x) = 5/x
Work done by A and B together in 10 days = (1/(3x)) * 10 = 10/(3x)
Remaining work after 10 days:
Total work - Work done by A, B, and A+B in 10 days = W - (10/x + 5/x + 10/(3x)) = W - (25/x + 10/(3x)) = W - (75 + 10)/(3x) = W - 85/(3x)
Now, C replaces B and starts working alone. Let's calculate the number of days C will take to complete the remaining work after 10 days:
Given that C can complete 1/20th of the work in 1 day. So, C will complete the remaining work in (W - 85/(3x)) * 20 days.
To find the day on which the project will be completed after C replaces B, we need to find the value of (W - 85/(3x)) * 20.
Let's simplify the expression:
(W - 85/(3x)) * 20 = (20W - (85/3x) * 20) = 20W - (1700/3x)
Since we are looking for the day on which the project will be completed, we need to find the integer value of (W - 85/(3x)) * 20.
Let's analyze the given options:
a) 15th day: (W - 85/(3x)) * 20 = 20W - (1700/3x) = 20W - (113.33/x)
b) 11th day: (W - 85/(3x)) * 20 = 20W - (1700/3x) = 20W - (1700/3x)
c) 9th day: (W - 85/(3x)) * 20 = 20W - (1700/3x) = 20W - (212.5/x)
d) 7th day
Efficiency of A:
Let the efficiency of A be 'x'. So, A can complete 1/xth of the work in 1 day.
Efficiency of B:
Given that the efficiency of B is twice that of A. So, the efficiency of B is '2x'. Hence, B can complete 1/(2x)th of the work in 1 day.
Efficiency of A and B together:
When A and B work together, their combined efficiency is the sum of their individual efficiencies. Hence, their combined efficiency is 'x + 2x = 3x'. Therefore, A and B together can complete 1/(3x)th of the work in 1 day.
Efficiency of C:
Given that C can complete the project alone in 20 days. So, the efficiency of C is 1/20th of the total work per day.
Let's calculate the work done by A, B, and A+B in 10 days:
Work done by A in 10 days = (1/x) * 10 = 10/x
Work done by B in 10 days = (1/(2x)) * 10 = 10/(2x) = 5/x
Work done by A and B together in 10 days = (1/(3x)) * 10 = 10/(3x)
Remaining work after 10 days:
Total work - Work done by A, B, and A+B in 10 days = W - (10/x + 5/x + 10/(3x)) = W - (25/x + 10/(3x)) = W - (75 + 10)/(3x) = W - 85/(3x)
Now, C replaces B and starts working alone. Let's calculate the number of days C will take to complete the remaining work after 10 days:
Given that C can complete 1/20th of the work in 1 day. So, C will complete the remaining work in (W - 85/(3x)) * 20 days.
To find the day on which the project will be completed after C replaces B, we need to find the value of (W - 85/(3x)) * 20.
Let's simplify the expression:
(W - 85/(3x)) * 20 = (20W - (85/3x) * 20) = 20W - (1700/3x)
Since we are looking for the day on which the project will be completed, we need to find the integer value of (W - 85/(3x)) * 20.
Let's analyze the given options:
a) 15th day: (W - 85/(3x)) * 20 = 20W - (1700/3x) = 20W - (113.33/x)
b) 11th day: (W - 85/(3x)) * 20 = 20W - (1700/3x) = 20W - (1700/3x)
c) 9th day: (W - 85/(3x)) * 20 = 20W - (1700/3x) = 20W - (212.5/x)
d) 7th day
Community Answer
A and B start working on a project. After 10 days B is replaced by C w...
A takes twice the time b takes to complete the work.
B takes 45 days. and A takes 90 days.
both A and B worked for 10 days that is equal to 1/3 rd of the work. hence 2/3rd work is remaining. both A and C will finish this work in 11 days
B takes 45 days. and A takes 90 days.
both A and B worked for 10 days that is equal to 1/3 rd of the work. hence 2/3rd work is remaining. both A and C will finish this work in 11 days
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A and B start working on a project. After 10 days B is replaced by C who can complete the project alone in 20 days. If A and B together can complete the project in 30 days, then find the day on which the project will be completed after C replaces B, if the efficiency of B is twice that of A.a)15th dayb)11th dayc)9th dayd)7th dayCorrect answer is option 'B'. Can you explain this answer?
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