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Mugdha and Mayuri, working together, can complete a job in 18 days. However, Mayuri works alone and leaves after completing two-fifths of the job and then Mugdha takes over and completes the remaining work by 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 worked faster than Mugdha?

Mugdha and Mayuri, working together, can complete a job in 18 days. However, Mayuri works alone and leaves after completing two-fifths of the job and then Mugdha takes over and completes the remaining work by 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 worked faster than Mugdha? Correct Answer 45

Mugdha and Mayuri, working together, can complete a job in 18 days,

⇒ 1 day work of Mughda and Mayuri = 1/18

Let Mayuri take x days to complete a work,

⇒ 1 day work of Mayuri = 1/x

Let Mugdha take y days to complete a work,

⇒ 1 day work of Mugdha = 1/y

⇒ 1/x + 1/y = 1/18      ----(1)

Mayuri works alone and leaves after completing two-fifths of the job and then Mugdha takes over and completes the remaining work by herself. As a result, the duo could complete the job in 39 days,

⇒ 2/5x + 3/5y = 39      ----(2)

Solving equation 1 and 2,

From equation 1,

⇒ 18x + 18y = xy

⇒ 18y = xy – 18x

⇒ x = 18y/ (y – 18)

Substituting value of y in equation 2,

⇒ 2/5 × 1/ + 3y/5 = 39

⇒ 36y/5 + 3y/5 = 39

⇒ 36y + 3y = 39 × 5

⇒ 36y + 3y2 – 54y = 195y – 3510

⇒ 3y2 – 213y + 3510 = 0

⇒ y2 – 71y + 1170 = 0

⇒ (y – 26) (y – 45) = 0

⇒ y = 26 or 45

Substituting in equation 1,

When y = 26, x = 58.5 and when y = 45, x = 30

Since, Mayuri worked faster,

∴ Mugdha takes 45 days

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