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
Question
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
Solution
First, let's find out how much work A, B, and C can do in one day.
A can complete the job in 16 days, so A can do 1/16 of the job in one day. B can complete the job in 12 days, so B can do 1/12 of the job in one day.
When A, B, and C work together, they can complete the job in 4 days. So, they can do 1/4 of the job in one day.
Let's denote the amount of work C can do in one 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 multiply each term by 48:
3 + 4 + 48/C = 12
Combine like terms:
7 + 48/C = 12
Subtract 7 from both sides:
48/C = 5
Finally, solve for C by dividing both sides by 5:
C = 48/5 = 9.6
So, C alone can do the job in 9.6 days.
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