Math, asked by mohanpahva1821, 1 year ago

Sharan and mayaukh working together can complete a task in 18 days. However mayukh works alone and leaves after completing one third of the task. Then, s

Answers

Answered by saiyam93
0
then 67 % of work is donwe by sharqn
Answered by TooFree
3

Answer:

(c) 45 days


Step-by-step explanation:

Define x and y:

Let x be the number of days mayukh takes to complete the work alone.

1 day = 1/x of the work


Let y be the number of days Sharan takes to complete the work alone.

1 day = 1/y of the work


They took 18 days if they work together:

1/x + 1/y = 1/18


Makyukh completed 1/3 of the work:

Number of days needed = 1/3 (x)


Sharan completed the the remaining of the work:

Remaining of the work = 1 - 1/3 = 2/3

Number of days needed = 2/3 (y)


They took 40 days:

1/3 (x) + (2/3) y = 40 days

x + 2y = 120 days


1/x + 1/y = 18 ------------------- [ 1 ]

x + 2y = 120 ------------------- [ 2 ]


From [ 1 ] :

1/x + 1/y = 18

(x + y)/xy = 1/18

18(x + y) = xy

18x + 18y = xy

18y = xy - 18x

18y = x(y - 18)

x = 18y/(y - 18)  ------------ sub into [ 2 ]


18y/(y - 18) + 2y = 120

18y + 2y(y -18) = 120 (y - 18)

18y + 2y² - 36y = 120y - 2160

2y² - 138y + 2160 = 0

y² - 69y + 1080= 0

(y - 24)(y - 45) = 0

y = 24 or y = 45


When y = 24,

x + 2y = 120

x + 2(24) = 120

x = 120 - 48 = 72


When y = 45,

x + 2(45) = 120

x = 120 - 90 = 30


Find the days taken by each of them

Mayukh = 72 days, Sharan = 24 days

Mayukh = 30 days, Sharan = 45 days


Since we know that Mayukh works faster

⇒ Sharan will need 45 days


Answer: (C) 45 days

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