.Sharan and Mayukh, working together, can complete a task in 18 days. However, Mayukh works alone and leaves after completing one-third of the task. Then, Sharan takes over and completes the remaining work by himself. As a result, the duo could complete the task in 40 days. How many days would Sharan alone have taken to do the job if Mayukh had worked faster than Sharan?
A) 42 days
B) 40 days
C) 45days
D) 48day
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
Answer:
Step-by-step explanation:
Let Mayukh -x, sharan-y Sharan<Mayukh,let 1/3x +2/3y= 40, ...1 given condition , x+y =18.......2 ,. By solving 1 and 2. X=30, 72 y=45, 24. He asked for Sharan ........we take..45days .....because...Mayukh > Sharan efficiency.............so ans 45 days