A takes 10 days less than the time taken by B to finish a piece of work. If both A and B can do it in 12 days, then the time taken by B alone to finish the work is?Options30 days20 days25 days27 days
Question
A takes 10 days less than the time taken by B to finish a piece of work. If both A and B can do it in 12 days, then the time taken by B alone to finish the work is?Options30 days20 days25 days27 days
Solution
To solve this problem, we can use the concept of work and time.
Step 1: Let's assume the time taken by B alone to finish the work is 'x' days.
Step 2: According to the problem, A takes 10 days less than B to finish the work. So, A takes 'x-10' days to finish the work.
Step 3: We know that if A and B work together, they can finish the work in 12 days.
Step 4: The work done by A in 1 day is 1/(x-10) and the work done by B in 1 day is 1/x.
Step 5: The work done by A and B together in 1 day is 1/(x-10) + 1/x.
Step 6: According to the problem, A and B together can finish the work in 12 days. So, their combined work done in 1 day is 1/12.
Step 7: Equating the two, we get 1/(x-10) + 1/x = 1/12.
Step 8: Solving this equation, we get x = 20 days.
So, the time taken by B alone to finish the work is 20 days.
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