B is twice efficient than A and the total time taken to complete the work by both A and B together is 22 days. Find thenumber of days taken by B to complete the work alone.
Question
B is twice efficient than A and the total time taken to complete the work by both A and B together is 22 days. Find thenumber of days taken by B to complete the work alone.
Solution
Let's solve this step by step:
Step 1: Let's assume the amount of work to be 1 unit.
Step 2: Let's say A takes 'x' days to complete the work alone. So, A's work rate is 1/x.
Step 3: Since B is twice as efficient as A, B takes 'x/2' days to complete the work alone. So, B's work rate is 2/x.
Step 4: According to the problem, A and B together can complete the work in 22 days. So, their combined work rate is 1/22.
Step 5: We know that the combined work rate is the sum of the individual work rates. So, we can write the equation: 1/x + 2/x = 1/22.
Step 6: Solving this equation gives x = 44.
So, A alone can complete the work in 44 days and B, being twice as efficient, can complete the work alone in 44/2 = 22 days.
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