2.A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:9 1 days59 2 days59 3 days510
Question
2.A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:9 1 days59 2 days59 3 days510
Solution
First, let's find out how much work A, B and C can do in a day.
A can complete the job in 16 days, so A can do 1/16 of the job in a day. B can complete the job in 12 days, so B can do 1/12 of the job in a day.
Together, A, B and C can complete the job in 4 days, so they can do 1/4 of the job in a day.
Let's denote the amount of work C can do in a day as 1/C.
So, we have the equation:
1/16 + 1/12 + 1/C = 1/4
To solve for C, we first need to find a common denominator. The least common multiple of 16, 12, and 4 is 48, so we'll use that:
3/48 + 4/48 + 1/C = 12/48
Simplify the left side of the equation:
7/48 + 1/C = 12/48
Subtract 7/48 from both sides:
1/C = 5/48
Finally, to solve for C, we take the reciprocal of both sides:
C = 48/5 = 9.6
So, C alone can do the job in approximately 10 days.
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