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)A and B can do a piece of work in 72 days, B and C can do it in 120 days and A and C can do it in 90 days. In what time can A alone do it?
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)A and B can do a piece of work in 72 days, B and C can do it in 120 d...
To find out how long A alone can complete the work, we can first identify the work rates of A, B, and C using the given information.
Step 1: Calculate Individual Work Rates
- Let the total work be represented as 1 unit of work.
- Work Rates of Pairs:
- A and B can complete the work in 72 days:
Work rate of (A + B) = 1/72 units per day
- B and C can complete the work in 120 days:
Work rate of (B + C) = 1/120 units per day
- A and C can complete the work in 90 days:
Work rate of (A + C) = 1/90 units per day
Step 2: Setting Up Equations
Let:
- A's work rate = A
- B's work rate = B
- C's work rate = C
From the pairs:
- A + B = 1/72
- B + C = 1/120
- A + C = 1/90
Step 3: Solving the Equations
1. Add all three equations:
- (A + B) + (B + C) + (A + C) = 1/72 + 1/120 + 1/90
2. Combine like terms:
- 2A + 2B + 2C = 1/72 + 1/120 + 1/90
3. Finding a common denominator (360):
- 1/72 = 5/360
- 1/120 = 3/360
- 1/90 = 4/360
- Total = 5 + 3 + 4 = 12/360 = 1/30
4. Thus, 2(A + B + C) = 1/30, which gives A + B + C = 1/60
Step 4: Isolate A's Work Rate
- From A + B + C = 1/60, we can express A's work rate:
A = (1/60) - B - C
- Substitute B and C from previous equations to find A's work rate.
Step 5: Calculate A's Time Alone
After isolating A's rate and solving, we find:
A's work rate = 1/90, thus A can complete the work alone in:
- Time taken by A = 1 / (1/90) = 90 days.
Final Answer
Therefore, A alone can complete the work in 90 days.
Step 1: Calculate Individual Work Rates
- Let the total work be represented as 1 unit of work.
- Work Rates of Pairs:
- A and B can complete the work in 72 days:
Work rate of (A + B) = 1/72 units per day
- B and C can complete the work in 120 days:
Work rate of (B + C) = 1/120 units per day
- A and C can complete the work in 90 days:
Work rate of (A + C) = 1/90 units per day
Step 2: Setting Up Equations
Let:
- A's work rate = A
- B's work rate = B
- C's work rate = C
From the pairs:
- A + B = 1/72
- B + C = 1/120
- A + C = 1/90
Step 3: Solving the Equations
1. Add all three equations:
- (A + B) + (B + C) + (A + C) = 1/72 + 1/120 + 1/90
2. Combine like terms:
- 2A + 2B + 2C = 1/72 + 1/120 + 1/90
3. Finding a common denominator (360):
- 1/72 = 5/360
- 1/120 = 3/360
- 1/90 = 4/360
- Total = 5 + 3 + 4 = 12/360 = 1/30
4. Thus, 2(A + B + C) = 1/30, which gives A + B + C = 1/60
Step 4: Isolate A's Work Rate
- From A + B + C = 1/60, we can express A's work rate:
A = (1/60) - B - C
- Substitute B and C from previous equations to find A's work rate.
Step 5: Calculate A's Time Alone
After isolating A's rate and solving, we find:
A's work rate = 1/90, thus A can complete the work alone in:
- Time taken by A = 1 / (1/90) = 90 days.
Final Answer
Therefore, A alone can complete the work in 90 days.
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)A and B can do a piece of work in 72 days, B and C can do it in 120 days and A and C can do it in 90 days. In what time can A alone do it?
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)A and B can do a piece of work in 72 days, B and C can do it in 120 days and A and C can do it in 90 days. In what time can A alone do it? for SSC CHSL 2025 is part of SSC CHSL preparation. The Question and answers have been prepared according to the SSC CHSL exam syllabus. Information about )A and B can do a piece of work in 72 days, B and C can do it in 120 days and A and C can do it in 90 days. In what time can A alone do it? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for )A and B can do a piece of work in 72 days, B and C can do it in 120 days and A and C can do it in 90 days. In what time can A alone do it?.
)A and B can do a piece of work in 72 days, B and C can do it in 120 days and A and C can do it in 90 days. In what time can A alone do it? for SSC CHSL 2025 is part of SSC CHSL preparation. The Question and answers have been prepared according to the SSC CHSL exam syllabus. Information about )A and B can do a piece of work in 72 days, B and C can do it in 120 days and A and C can do it in 90 days. In what time can A alone do it? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for )A and B can do a piece of work in 72 days, B and C can do it in 120 days and A and C can do it in 90 days. In what time can A alone do it?.
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