RRB NTPC/ASM/CA/TA Exam > RRB NTPC/ASM/CA/TA Questions > Two teachers A and B can complete an academic...
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Two teachers A and B can complete an academic work in 10 days and 15 days respectively. They started the work together, but A left after 5 days and another teacher C joined, who alone can complete the work in 60 days. In how many days the work got completed?
- a)7
- b)5
- c)6
- d)2
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Two teachers A and B can complete an academic work in 10 days and 15 d...
Let total work be 60x units (LCM of 10,15,60 )
Efficiency of A = 6x units/day
Efficiency of B = 4x units/day
Efficiency of C = x units/day
Work done in 5 days by A and B = (6x+4x)×5 = 50x units
Remaining work = 60x − 50x = 10x units
This work is completed by B and C.
Time taken to complete the remaining work = 10x/(4x+x)
= 10x/5x
= 2 days
∴ Total time taken to complete the work = 5 + 2 = 7 days
Efficiency of A = 6x units/day
Efficiency of B = 4x units/day
Efficiency of C = x units/day
Work done in 5 days by A and B = (6x+4x)×5 = 50x units
Remaining work = 60x − 50x = 10x units
This work is completed by B and C.
Time taken to complete the remaining work = 10x/(4x+x)
= 10x/5x
= 2 days
∴ Total time taken to complete the work = 5 + 2 = 7 days
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Two teachers A and B can complete an academic work in 10 days and 15 d...
Given:
Teacher A can complete the work in 10 days.
Teacher B can complete the work in 15 days.
Teacher C can complete the work in 60 days.
Approach:
1. Find the efficiency of each teacher.
2. Use the concept of work done to find the total work done by teachers A and B in 5 days.
3. Find the remaining work.
4. Use the concept of work done to find the total work done by teachers B and C in the remaining days.
5. Find the total time taken to complete the work.
Solution:
Step 1: Find the efficiency of each teacher
The efficiency of a person is inversely proportional to the number of days taken to complete the work.
Efficiency of teacher A = 1/10 (as A can complete the work in 10 days)
Efficiency of teacher B = 1/15 (as B can complete the work in 15 days)
Efficiency of teacher C = 1/60 (as C can complete the work in 60 days)
Step 2: Find the work done by teachers A and B in 5 days
The total work done by teachers A and B in 5 days can be calculated by multiplying their efficiencies by the number of days.
Work done by teacher A in 5 days = (1/10) * 5 = 1/2
Work done by teacher B in 5 days = (1/15) * 5 = 1/3
Step 3: Find the remaining work
The remaining work can be calculated by subtracting the work done by teachers A and B in 5 days from the total work.
Remaining work = 1 - (1/2 + 1/3) = 1 - (3/6 + 2/6) = 1 - (5/6) = 1/6
Step 4: Find the work done by teachers B and C in the remaining days
The work done by teachers B and C in the remaining days can be calculated by multiplying their efficiencies by the number of days.
Let the number of days taken to complete the remaining work be x.
Work done by teacher B in x days = (1/15) * x
Work done by teacher C in x days = (1/60) * x
The sum of their work done should be equal to the remaining work.
(1/15) * x + (1/60) * x = 1/6
Simplifying the equation, we get:
(4x + x)/60 = 1/6
5x/60 = 1/6
5x = 10
x = 2
So, the remaining work can be completed by teachers B and C in 2 days.
Step 5: Find the total time taken to complete the work
The total time taken to complete the work is the sum of the time taken by teacher A (5 days) and the time taken by teachers B and C (2 days).
Total time taken = 5 + 2 = 7 days
Therefore, the work got completed in 7 days.
Hence, the correct answer is option A) 7.
Teacher A can complete the work in 10 days.
Teacher B can complete the work in 15 days.
Teacher C can complete the work in 60 days.
Approach:
1. Find the efficiency of each teacher.
2. Use the concept of work done to find the total work done by teachers A and B in 5 days.
3. Find the remaining work.
4. Use the concept of work done to find the total work done by teachers B and C in the remaining days.
5. Find the total time taken to complete the work.
Solution:
Step 1: Find the efficiency of each teacher
The efficiency of a person is inversely proportional to the number of days taken to complete the work.
Efficiency of teacher A = 1/10 (as A can complete the work in 10 days)
Efficiency of teacher B = 1/15 (as B can complete the work in 15 days)
Efficiency of teacher C = 1/60 (as C can complete the work in 60 days)
Step 2: Find the work done by teachers A and B in 5 days
The total work done by teachers A and B in 5 days can be calculated by multiplying their efficiencies by the number of days.
Work done by teacher A in 5 days = (1/10) * 5 = 1/2
Work done by teacher B in 5 days = (1/15) * 5 = 1/3
Step 3: Find the remaining work
The remaining work can be calculated by subtracting the work done by teachers A and B in 5 days from the total work.
Remaining work = 1 - (1/2 + 1/3) = 1 - (3/6 + 2/6) = 1 - (5/6) = 1/6
Step 4: Find the work done by teachers B and C in the remaining days
The work done by teachers B and C in the remaining days can be calculated by multiplying their efficiencies by the number of days.
Let the number of days taken to complete the remaining work be x.
Work done by teacher B in x days = (1/15) * x
Work done by teacher C in x days = (1/60) * x
The sum of their work done should be equal to the remaining work.
(1/15) * x + (1/60) * x = 1/6
Simplifying the equation, we get:
(4x + x)/60 = 1/6
5x/60 = 1/6
5x = 10
x = 2
So, the remaining work can be completed by teachers B and C in 2 days.
Step 5: Find the total time taken to complete the work
The total time taken to complete the work is the sum of the time taken by teacher A (5 days) and the time taken by teachers B and C (2 days).
Total time taken = 5 + 2 = 7 days
Therefore, the work got completed in 7 days.
Hence, the correct answer is option A) 7.
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