RRB NTPC/ASM/CA/TA Exam > RRB NTPC/ASM/CA/TA Questions > The efficiency ofA,B, andCis2:3:5.A alone can...
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The efficiency of A,B, and C is 2:3:5. A alone can complete a work in 50 days. They all work together for 5 days and then C left the work, in how many days A and B together can complete the remaining work?
- a)50 days
- b)30 days
- c)20 days
- d)10 days
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
The efficiency ofA,B, andCis2:3:5.A alone can complete a work in 50 da...
Given:
Efficiency of A,B and C=2:3:5
A alone can complete the work in =50 days
Total work = Efficiency × Time
Let efficiency of A be 2 units / day
Efficiency of A,B and C=2:3:5
Total work =2×50=100 units
Work done by A,B and C in 5 days =(2+3+5)×5=10×5=50 units
Remaining work =100−50=50 units
∴ Time taken by A and B to complete the remaining work =
Efficiency of A,B and C=2:3:5
A alone can complete the work in =50 days
Total work = Efficiency × Time
Let efficiency of A be 2 units / day
Efficiency of A,B and C=2:3:5
Total work =2×50=100 units
Work done by A,B and C in 5 days =(2+3+5)×5=10×5=50 units
Remaining work =100−50=50 units
∴ Time taken by A and B to complete the remaining work =
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The efficiency ofA,B, andCis2:3:5.A alone can complete a work in 50 da...
Understanding the Efficiency Ratio
The efficiency ratio of A, B, and C is given as 2:3:5. This means:
- A's work efficiency = 2x
- B's work efficiency = 3x
- C's work efficiency = 5x
Since A can complete the work in 50 days, the total work (W) can be calculated as:
- W = A's efficiency * Time taken by A = 2x * 50 = 100x
Calculating Individual Efficiencies
From the total work:
- A's efficiency = 2x = 100/50 = 2 units/day
- B's efficiency = 3x = 3/2 * 2 = 3 units/day
- C's efficiency = 5x = 5/2 * 2 = 5 units/day
Now, the total efficiency of A, B, and C working together:
- Total efficiency = A + B + C = 2 + 3 + 5 = 10 units/day
Work Done Together in 5 Days
In 5 days, the combined work done by A, B, and C is:
- Work done = Total efficiency * Days = 10 units/day * 5 days = 50 units
Remaining Work Calculation
Remaining work after 5 days:
- Remaining work = Total work - Work done = 100x - 50 = 50 units
A and B Working Together
Now, A and B will work together to complete the remaining 50 units. Their combined efficiency is:
- A + B = 2 + 3 = 5 units/day
Time Taken by A and B
Time taken to complete the remaining work:
- Time = Remaining work / Combined efficiency = 50 units / 5 units/day = 10 days
Thus, A and B together can complete the remaining work in 10 days.
Correct answer: Option D: 10 days.
The efficiency ratio of A, B, and C is given as 2:3:5. This means:
- A's work efficiency = 2x
- B's work efficiency = 3x
- C's work efficiency = 5x
Since A can complete the work in 50 days, the total work (W) can be calculated as:
- W = A's efficiency * Time taken by A = 2x * 50 = 100x
Calculating Individual Efficiencies
From the total work:
- A's efficiency = 2x = 100/50 = 2 units/day
- B's efficiency = 3x = 3/2 * 2 = 3 units/day
- C's efficiency = 5x = 5/2 * 2 = 5 units/day
Now, the total efficiency of A, B, and C working together:
- Total efficiency = A + B + C = 2 + 3 + 5 = 10 units/day
Work Done Together in 5 Days
In 5 days, the combined work done by A, B, and C is:
- Work done = Total efficiency * Days = 10 units/day * 5 days = 50 units
Remaining Work Calculation
Remaining work after 5 days:
- Remaining work = Total work - Work done = 100x - 50 = 50 units
A and B Working Together
Now, A and B will work together to complete the remaining 50 units. Their combined efficiency is:
- A + B = 2 + 3 = 5 units/day
Time Taken by A and B
Time taken to complete the remaining work:
- Time = Remaining work / Combined efficiency = 50 units / 5 units/day = 10 days
Thus, A and B together can complete the remaining work in 10 days.
Correct answer: Option D: 10 days.
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