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A and B can do a piece of work in 20 and 25 days respectively. They began to work together but A leaves after some days and B completed the remaining work in 12 days. Number of days after which A left the job

  • a)
    52/9 days

  • b)
    67/9 days

  • c)
    77/9 days

  • d)
    117/9 days

  • e)
    None of these

Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A and B can do a piece of work in 20 and 25 days respectively. They be...
(1/20 + 1/25)*T + 12/25 = 1

We will get T = 52/9  days
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Most Upvoted Answer
A and B can do a piece of work in 20 and 25 days respectively. They be...
Let's assume that the total work is represented by the variable 'W'.

A can complete the work in 20 days, which means that in one day, A can complete 1/20th of the work. Similarly, B can complete the work in 25 days, so in one day, B can complete 1/25th of the work.

When A and B work together, their combined work rate is the sum of their individual work rates. So the combined work rate of A and B is (1/20 + 1/25) = 9/100.

Let's say A worked for 'x' days before leaving the job. During this time, A completed x/20th of the work. The remaining work is (1 - x/20) = (20 - x)/20.

After A leaves, B completes the remaining work in 12 days. So B's work rate is (20 - x)/20 * 1/12 = 1.

Simplifying the equation, we get (20 - x)/240 = 1.

Cross-multiplying, we get 20 - x = 240.

Solving for x, we get x = 220.

Therefore, A left the job after 220 days.

To convert this into a fraction, we divide 220 by the total number of days A and B worked together, which is 20.

So, the answer is 220/20 = 11/9 days.

The correct option is (a) 5.7/9 days.
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Community Answer
A and B can do a piece of work in 20 and 25 days respectively. They be...
X/20 + (X+12)/25 =1

= 5 7/9
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A and B can do a piece of work in 20 and 25 days respectively. They began to work together but A leaves after some days and B completed the remaining work in 12 days. Number of days after which A left the joba)52/9 daysb)67/9 daysc)77/9 daysd)117/9 dayse)None of theseCorrect answer is option 'A'. Can you explain this answer?
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