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A and B together can do a piece of work in 7(1/5) days, B and C together can do the same piece of work in 10(2/7) days. A, B and C working together can complete the work in 4(1/2) days. In what time B working alone can complete the work?
- a)18 days
- b)24 days
- c)72 days
- d)36 days
- e)48 days
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A and B together can do a piece of work in 7(1/5)days, B and C togethe...
GIVEN :
A and B together can do a piece of work in 36/5 days.
B and C together can do a piece of work in 72/7 days.
A, B and C together can do a piece of work in 9/2 days.
CALCULATION :
⇒ One day work of (A + B) = 5/36
⇒ One day work of (B + C) = 7/72
⇒ One day work of (A + B + C) = 2/9
One day work A = One day work of (A + B + C) - One day work work of (B + C)
⇒ 2/9 - 7/72
⇒ 1/8
One day work of C = One day work of (A + B + C) - One day work work of (A + B)
⇒ 2/9 - 5/36
⇒ 1/12
One day work of (A + C) = 1/8 + 1/12 = 5/24
One day work of B = One day work of (A + B + C) - One day work work of (A + C)
⇒ 2/9 - 5/24
⇒ 1/72
∴ B alone can complete the work in 72 days.
A and B together can do a piece of work in 36/5 days.
B and C together can do a piece of work in 72/7 days.
A, B and C together can do a piece of work in 9/2 days.
CALCULATION :
⇒ One day work of (A + B) = 5/36
⇒ One day work of (B + C) = 7/72
⇒ One day work of (A + B + C) = 2/9
One day work A = One day work of (A + B + C) - One day work work of (B + C)
⇒ 2/9 - 7/72
⇒ 1/8
One day work of C = One day work of (A + B + C) - One day work work of (A + B)
⇒ 2/9 - 5/36
⇒ 1/12
One day work of (A + C) = 1/8 + 1/12 = 5/24
One day work of B = One day work of (A + B + C) - One day work work of (A + C)
⇒ 2/9 - 5/24
⇒ 1/72
∴ B alone can complete the work in 72 days.
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A and B together can do a piece of work in 7(1/5)days, B and C togethe...
Understanding the Problem
To determine how long B alone would take to complete the work, we start by converting the mixed fractions into improper fractions.
Work Rates of A, B, and C
- A and B together complete the work in 7(1/5) days, which is 36/5 days. Therefore, their combined work rate is 5/36 (work per day).
- B and C together complete the work in 10(2/7) days, which is 72/7 days. Thus, their combined work rate is 7/72 (work per day).
- A, B, and C together complete the work in 4(1/2) days, which is 9/2 days. Hence, their combined work rate is 2/9 (work per day).
Setting Up the Equations
Let the work rates of A, B, and C be a, b, and c respectively. We can set up the following equations based on the rates:
1. a + b = 5/36
2. b + c = 7/72
3. a + b + c = 2/9
Finding Individual Work Rates
From the third equation, we can express c in terms of a and b:
c = (2/9) - (a + b)
Substituting a + b from the first equation:
c = (2/9) - (5/36)
Converting (2/9) to a common denominator (36):
c = (8/36) - (5/36) = 3/36 = 1/12
Now substitute c back into the second equation:
b + (1/12) = 7/72
Converting (1/12) to common denominator (72):
b + (6/72) = 7/72
Thus, b = (7/72) - (6/72) = 1/72.
Calculating Time for B Alone
The time taken by B to complete the work alone is the reciprocal of b:
Time = 1 / (1/72) = 72 days.
Thus, the correct answer is option 'C': 72 days.
To determine how long B alone would take to complete the work, we start by converting the mixed fractions into improper fractions.
Work Rates of A, B, and C
- A and B together complete the work in 7(1/5) days, which is 36/5 days. Therefore, their combined work rate is 5/36 (work per day).
- B and C together complete the work in 10(2/7) days, which is 72/7 days. Thus, their combined work rate is 7/72 (work per day).
- A, B, and C together complete the work in 4(1/2) days, which is 9/2 days. Hence, their combined work rate is 2/9 (work per day).
Setting Up the Equations
Let the work rates of A, B, and C be a, b, and c respectively. We can set up the following equations based on the rates:
1. a + b = 5/36
2. b + c = 7/72
3. a + b + c = 2/9
Finding Individual Work Rates
From the third equation, we can express c in terms of a and b:
c = (2/9) - (a + b)
Substituting a + b from the first equation:
c = (2/9) - (5/36)
Converting (2/9) to a common denominator (36):
c = (8/36) - (5/36) = 3/36 = 1/12
Now substitute c back into the second equation:
b + (1/12) = 7/72
Converting (1/12) to common denominator (72):
b + (6/72) = 7/72
Thus, b = (7/72) - (6/72) = 1/72.
Calculating Time for B Alone
The time taken by B to complete the work alone is the reciprocal of b:
Time = 1 / (1/72) = 72 days.
Thus, the correct answer is option 'C': 72 days.
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A and B together can do a piece of work in 7(1/5)days, B and C together can do the same piece of work in 10(2/7)days. A, B and C working together can complete the work in 4(1/2)days. In what time B working alone can complete the work?a)18 daysb)24 daysc)72 daysd)36 dayse)48 daysCorrect answer is option 'C'. Can you explain this answer?
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