A is thrice as good as B and he is able to finish the work 60 days less than B. In how many days they will finish the same work together
Question
A is thrice as good as B and he is able to finish the work 60 days less than B. In how many days they will finish the same work together?
Solution
To solve this problem, we need to understand the concept of work and efficiency in time and work problems.
Step 1: Define the variables Let's say B takes 'x' days to complete the work alone.
Step 2: Define the relationship According to the problem, A is thrice as good as B. This means A can complete the work in 1/3 of the time B takes. So, A takes 'x/3' days to complete the work.
Step 3: Use the given information The problem also states that A is able to finish the work 60 days less than B. So, we can write the equation as: x - 60 = x/3
Step 4: Solve the equation Multiplying all terms by 3 to clear the fraction, we get: 3x - 180 = x Subtracting x from both sides, we get: 2x = 180 Dividing both sides by 2, we get: x = 90
So, B takes 90 days to complete the work and A, being thrice as efficient, takes 30 days to complete the same work.
Step 5: Find the time they take to complete the work together When two people work together, their combined work rate is the sum of their individual work rates. So, if A completes 1 work in 30 days and B completes 1 work in 90 days, together they complete 1/30 + 1/90 = 4/90 of the work in a day.
Therefore, to complete 1 work, they will take 90/4 = 22.5 days.
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