plzz give me answer
Answers
Answer:
10 days, 15 days
Step-by-step explanation:
Given:
Sunil takes 5 days more than Anil to complete a certain work. 4 days after starting the work, Anil left the work. The remaining work was done by Sunil in 5 days.
To Find:
How many days each will take to complete the work.
Solution:
Let Anil takes x days to complete the work and Sunil takes x+5 days.
In 1 day Anil work = 1/x and,
In 1 day Sunil work = 1/ x+5.
Together they work for 4 days.
In 4 days they would have completed (4/x )+ 4/(x+5) of the job.
LCM =x (x+5)
==> (4 (x+5) + 4x)/x(x + 5)
==> 4x+20+4x/x (x +5)
Remaining Work is completed by Sunil in 5 days.
In 5 days he does 5/(x+5) and completes the work.
So the whole equation becomes:
8x+20/x (x+5) + 5/(x+5) = 1
==> 8x + 20 + 5x = x^2 + 5x
==> 8x + 20 - x^2 =0
==> x^2 - 8x -20 = 0
==> x^2 - 10x +2x - 20 = 0
==> x = 10 or -2 ( rejected)
==> x = 10 days
Thus,
x + 5 = 15 days.
Result :
Anil takes 10 days and Sunil takes 15 days.