mugdha and mayuri working together can complete a job in 18 days. however mayuri works alone and leaves after completing two-fifths of the jobs and then. mugdha takes over and completes the remaining works bye herself. as a result the duo could complete the job in 39 days how many days would mugdha alone have taken to do the job if mayuri works faster than mugdha ?
Answers
Answer:
45 days
Step-by-step explanation:
Mugdha and Mayuri working together can complete a job in 18 days
⇒ 1 day = 1/18 of the work
They can do 1/18 of the work in 1 day
Define x:
Let Mayuri take x days to complete the work alone
⇒ 1 day = 1/x of the work
Mayuri can do 1/x of the work in 1 day
Let Mugdha take y days to complete the work alone
⇒ 1 day = 1/y of the work
Mugdha can do 1/y of the work in 1 day
Mayuri did 2/5 of the work and Mugdha did 3/5 of the work, they took 39 days.
⇒ 2/5 x + 3/5 y = 39
Solve for x and y:
1/x + 1/y = 1/18 ---------------- [ 1 ]
2/5 x + 3/5 y = 39 ---------------- [ 2 ]
From [ 1 ]:
1/x + 1/y = 1/18
y + x = xy/18
18y + 18x = xy
18y = xy - 18x
18y = x( y - 18)
x = 18y/(y - 18) -------------- Sub into [ 2 ]:
From [ 2 ]:
2/5 x + 3/5 y = 39
2/5 (18y/(y - 18)) + 3y/5 = 39
36y/5(y - 18) + 3y/5 = 39
36y + 3y(y - 18) = 39(5(y - 18))
36y + 3y² - 54y = 195y - 3510
3y² - 213y + 3510 = 0
y² - 71y + 1170 = 0
(y - 26) (y - 45) = 0
y = 26 or y = 45 ----------- sub in [ 1 ]
When y = 26
1/x + 1/y = 1/18
1/x + 1/26 = 1/18
1/x = 2/117
x = 117 ÷ 2 = 58.5
When y = 45,
1/x + 1/y = 1/18
1/x + 1/45 = 1/18
1/x = 1/30
x = 30
If Mayuri takes 58.5 days, Mugdha takes 26 days
If Mayuri takes 30 days, Mugdha takes 45 days
Since it is mentioned that Mayuri works faster,
therefore Mayuri takes 30 days, Mugdha takes 45 days
Answer: Mugdha will take 45 days
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