Question

Nitin and Jitin work together, they will complete a job in 40 3 days. If Nitin works alone and completes half the job and then Jitin takes over and completes the rest half of the job, then the total time taken by both of them is 30 days. How long will it take Jitin to complete the job alone, if Nitin is more efficient than Jitin?

Answer 1

Step-by-step explanation:

Given  

Nitin and Jitin work together, they will complete a job in 40 3 days. If Nitin works alone and completes half the job and then Jitin takes over and completes the rest half of the job, then the total time taken by both of them is 30 days. How long will it take Jitin to complete the job alone, if Nitin is more efficient than Jitin?

• Let Nitin completes job in x days
• Let Jitin completes job in y days
• So 1 day work of Nitin is 1/x
• 1 day work of Jitin is 1/y
• So 3/40 = 1 / x + 1 / y --------------- 1
• According to question a / x = 1 / 2
• Or a = x/2 --------------2
• Also b / y = 1/2  
• Or b = y / 2-------------3
• Now a + b = 30
• So x / 2 + y / 2 = 30
• Or x + y = 60 or y = 60 – x
• So 3/40 = 1/x + 1/y
•             = x + y / xy
• Or 3/40 = 60 / xy
• So xy = 800
• Now x (60 – x) = 800
• So x^2 – 60 x + 800 = 0
• So x^2 – 40a – 20a + 800 = 0
• So x(x – 40) – 20(x – 40) = 0
• So x – 40 = 0, x – 20 = 0
• Or x = 40 , 20
• Now x < y
• So x + y = 60
•     20 + y = 60
• Or y = 40
• So x + y = 60
• Or x + 40 = 60
• Or x = 20

So Jitin will be able to complete the work in 40 days

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