Pooja is twice as efficient as Aarti and takes 90 days less than Aarti to complete the job. Find the time in which they can finish the job together.
If Pooja takes x days, then Aarti takes 2x days. So,
x = 2x-90
x = 90
Now, if they take n days together, then
1/90 + 1/180 = 1/n
Solve for n
Thank you
Let's assume that Aarti takes x days to complete the job.
Since Pooja is twice as efficient as Aarti, she can complete the job in x/2 days.
Given that Pooja takes 90 days less than Aarti to complete the job, we can set up the equation:
x - 90 = x/2
To solve for x, we can multiply the entire equation by 2 to get rid of the fraction:
2(x - 90) = x
Expanding and simplifying the equation:
2x - 180 = x
Subtracting x from both sides:
2x - x = 180
x = 180
Therefore, Aarti takes 180 days to complete the job.
To find the time they can finish the job together, we can add the times they take individually:
180 + (180/2) = 180 + 90 = 270
Therefore, Pooja and Aarti can finish the job together in 270 days.
To solve this problem, we'll need to understand the concept of work efficiency and use the formula related to it.
Let's assume that the total work to be done is represented by W, and let x be the number of days it takes Aarti to complete the job.
Given that Pooja is twice as efficient as Aarti, we can say that Pooja completes the job in x/2 days.
It is also given that Pooja takes 90 days less than Aarti to complete the job. So, we can set up the equation:
x - 90 = x/2
To solve the equation, we'll start by multiplying both sides by 2 to get rid of the fraction:
2x - 180 = x
Next, subtract x from both sides to isolate x:
2x - x = 180
x = 180
So, Aarti takes 180 days to complete the job.
To find the time in which they can finish the job together (let's call it t), we can set up the equation:
1/x + 1/(x/2) = 1/t
Substituting the value of x, we get:
1/180 + 1/(180/2) = 1/t
Simplifying further:
1/180 + 2/180 = 1/t
3/180 = 1/t
Multiplying both sides by 180 to isolate t:
3 = 180/t
Dividing both sides by 3:
t = 180/3
Therefore, Aarti and Pooja can finish the job together in 60 days.