A takes 5 days more than B to do a certain job and 9 days more than C; A and B can do the job in the same time as C. How many days A would take to do it?Options5152010
Question
A takes 5 days more than B to do a certain job and 9 days more than C; A and B can do the job in the same time as C. How many days A would take to do it?Options5152010
Solution
Let's denote the time it takes for A, B, and C to complete the job as a, b, and c respectively.
From the problem, we know that:
- a = b + 5 (A takes 5 days more than B to do a certain job)
- a = c + 9 (A takes 9 days more than C to do the job)
- a + b = c (A and B can do the job in the same time as C)
We can substitute equations 1) and 2) into equation 3) to get:
b + 5 + b = c + 9 2b = c + 4 c = 2b - 4
Substitute c into equation 2):
a = 2b - 4 + 9 a = 2b + 5
Since a = b + 5, we can set 2b + 5 = b + 5 and solve for b:
b = 0
Substitute b = 0 into a = b + 5:
a = 0 + 5 a = 5
So, A would take 5 days to do the job. The answer is 5.
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