Question

when aman alone does a piece of work, he takes 16 days more than the time taken by aman andajeet to complete the work, while ajeet alone takes 9 days more than the time take by both tofinish the work. what time, both will take to finish this work?

Answer 1

The time taken by Aman and Ajeet to finish the work together is 12 days, which can be found by setting up an equation based on their combined work rates and solving for the variable representing the time they take together.

Step-by-step explanation:

Let's denote the time taken by both Aman and Ajeet together to finish the work as x days. Then, Aman takes x + 16 days to finish the work alone, while Ajeet takes x + 9 days to finish the work alone.
We can set up the work rate for each of them as follows: Aman's rate is 1/(x + 16) work per day, and Ajeet's rate is 1/(x + 9) work per day. When working together, their combined rate is 1/x work per day. According to the information given, the sum of their individual rates is equal to their combined rate when working together:

1/(x + 16) + 1/(x + 9) = 1/x

To find the value of x, we should solve this equation:
Start by finding a common denominator and then add the fractions:

(x + 9 + x + 16) / ((x + 16)(x + 9)) = 1/x

Simplify the equation:

(2x + 25) / ((x + 16)(x + 9)) = 1/x

To clear the fractions, we multiply both sides by x(x + 16)(x + 9):

x(2x + 25) = (x + 16)(x + 9)

Now expand both sides:

2x^2 + 25x = x^2 + 25x + 144

Subtract x^2 + 25x from both sides of the equation:

x^2 = 144

Finally, finding the square root gives us:

x = 12

So, both Aman and Ajeet together complete the work in 12 days.