Select the correct answerA and B together can finish a work in 5 days. If A works twice his efficiency they can finish the same work in 3 days. In how many days will A alone finish the work?Options5.4 days7.5 days6.6 days15 days
Question
Select the correct answerA and B together can finish a work in 5 days. If A works twice his efficiency they can finish the same work in 3 days. In how many days will A alone finish the work?Options5.4 days7.5 days6.6 days15 days
Solution
To solve this problem, we need to understand the concept of work and efficiency.
Step 1: Let's denote the efficiency of A as 'a' and the efficiency of B as 'b'. The efficiency of a person is the amount of work they can do in a day.
Step 2: From the problem, we know that A and B together can finish the work in 5 days. This means that (a+b)*5 = 1 work.
Step 3: We also know that if A works at twice his efficiency, they can finish the work in 3 days. This means that (2a+b)*3 = 1 work.
Step 4: Now we have a system of two equations, and we can solve it to find the values of 'a' and 'b'.
From (a+b)*5 = 1, we get a+b = 1/5.
From (2a+b)*3 = 1, we get 2a+b = 1/3.
Subtracting the first equation from the second, we get a = 1/3 - 1/5 = 2/15.
Step 5: Now that we know the efficiency of A, we can find out how many days A alone will finish the work. The time taken to complete a work is the reciprocal of efficiency.
So, A will finish the work in 1/a days = 1/(2/15) days = 15/2 days = 7.5 days.
So, the correct answer is 7.5 days.
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