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A can do 50% more work than B in same time. B alone can do a piece of work in 30 hours. B starts working and had already worked for 12 hours when A joins him. How many hours should B and A work together to complete the remaining work?
- a)16 hours
- b)12 hours
- c)4.8 hours
- d)7.2 hours
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A can do 50% more work than B in same time. B alone can do a piece of ...
B alone can do the work in 30 hours and A can do 50% more work than B in same time;
⇒ Time taken by A to complete the work alone = 30/1.5 = 20 hours
Suppose total work = 60 units (LCM of 20 & 30)
⇒ Time taken by A to complete the work alone = 30/1.5 = 20 hours
Suppose total work = 60 units (LCM of 20 & 30)
⇒ Efficiency of A = 60/20 = 3
⇒ Efficiency of B = 60/30 = 2
⇒ Unit of work done by B in 12 hours = 12 × 2 = 24 units
⇒ Remaining work = 60 – 24 = 36 units
∴ Time taken by (A + B) to complete remaining work = 36/5 = 7.2 hours
⇒ Efficiency of B = 60/30 = 2
⇒ Unit of work done by B in 12 hours = 12 × 2 = 24 units
⇒ Remaining work = 60 – 24 = 36 units
∴ Time taken by (A + B) to complete remaining work = 36/5 = 7.2 hours
Most Upvoted Answer
A can do 50% more work than B in same time. B alone can do a piece of ...
Given: A does 50% more work than B in the same time. B alone can do a piece of work in 30 hours. B starts working and had already worked for 12 hours when A joins him.
To find: How many hours should B and A work together to complete the remaining work?
Solution:
Let the total work be 1 unit.
B alone can do a piece of work in 30 hours, so B's 1 hour work = 1/30.
A does 50% more work than B in the same time, so A's 1 hour work = (1/30) x (150/100) = 1/20.
Total work done by B in 12 hours = (1/30) x 12 = 2/5.
Remaining work = 1 - 2/5 = 3/5.
Let the time taken by B and A working together to complete the remaining work be x hours.
So, the work done by B in x hours = (1/30) x x = x/30.
Work done by A in x hours = (1/20) x x = x/20.
Total work done by B and A together in x hours = x/30 + x/20 = 5x/60 = x/12.
According to the question, B had already worked for 12 hours when A joins him. So, the total time taken by B and A together to complete the work = 12 + x.
Now, we can form the equation:
2/5 + (x/12) = 3/5
Multiplying both sides by 60, we get:
24 + 5x = 36
5x = 12
x = 12/5 = 2.4 hours.
Therefore, B and A should work together for 2.4 hours to complete the remaining work.
Hence, the correct answer is option D.
To find: How many hours should B and A work together to complete the remaining work?
Solution:
Let the total work be 1 unit.
B alone can do a piece of work in 30 hours, so B's 1 hour work = 1/30.
A does 50% more work than B in the same time, so A's 1 hour work = (1/30) x (150/100) = 1/20.
Total work done by B in 12 hours = (1/30) x 12 = 2/5.
Remaining work = 1 - 2/5 = 3/5.
Let the time taken by B and A working together to complete the remaining work be x hours.
So, the work done by B in x hours = (1/30) x x = x/30.
Work done by A in x hours = (1/20) x x = x/20.
Total work done by B and A together in x hours = x/30 + x/20 = 5x/60 = x/12.
According to the question, B had already worked for 12 hours when A joins him. So, the total time taken by B and A together to complete the work = 12 + x.
Now, we can form the equation:
2/5 + (x/12) = 3/5
Multiplying both sides by 60, we get:
24 + 5x = 36
5x = 12
x = 12/5 = 2.4 hours.
Therefore, B and A should work together for 2.4 hours to complete the remaining work.
Hence, the correct answer is option D.
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