A and B can do a work together in 35 days. A complete its 5/7 part and remaining is done by B . that's how they completed it in 90 days. so how many days will A take to complete itself.l?
Answers
Let A take A days to complete the work and B, B days to complete the work.
In one day :
A does = 1/A of the work and B does 1/B of the work.
When they work together in one day they do :
1/A + 1/B
They complete the work in 35 days.
Therefore :
1/A + 1/B = 1/35........... 1)
When A does 5/7 of the work, he will take :
(5/7 × A/1) days to do the work.
= 5A/7
B will do 2/7 of the work and he will take %
= 2B/7 days
In total this is 90 days.
Therefore :
5A/7 + 2B/7 = 90........ 2)
Solving 1 and 2 simultaneously.
From 2 we have :
5A + 2B = 630
5A = 630 - 2B
A = 630/5 - 2/5B
A = 126 - 2/5B
Substituting A in 1.
1/(126 - 2/5B) + 1/B = 1/35
Multiplying through by (126 - 2/5B)
1 + (126 - 2/5B)/B = (126 - 2/5B) / 35
Multiplying through by B
B + 126 - 2/5B = B(126 - 2/5B)/35
Multiplying through by 35
35B + 4410 - 14B = 126B - 2/5B²
Multiplying through by 5
175B + 22050 - 70B = 630B - 2B²
Collecting the like terms together.
175B - 70B - 630B + 22050 + 2B² = 0
2B² - 525B + 22050 = 0
Solving the quadratic equation using the quadratic formula :
{525 √(525² - 4 × 2 × 22050)} /4
(525 +/- √99225) / 4
= (525 +/- 315)/4
B = 840/4 or 210/4
B = 210 or 52.5
We take 52.5 since it is more realistic.
We substitute this in 2 :
5A + 2 × 52.5 = 630
5A = 630 - 105
5A = 525
A = 525/5
A = 105 days
A working alone takes 105 days
Answer:
By Efficiency Method
Step-by-step explanation:
