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
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