Question

Siddharth, Nikita, Vinay and Neha individually takes different number of hours to complete a task. If Siddharth, Nikita and Vinay works together then they take 6 hours 40 minutes to complete the task and if Nikita, Vinay and Neha works together then they take 8 hours to complete the task. If Siddharth and Neha working together complete the task in 13 hours 20 minutes, then how much time will all the four persons take to complete the task working together?

• A. 4(\(\frac{4}{7}\)) hours.
• B. 5(\(\frac{3}{7}\)) hours.
• C. 5(\(\frac{5}{7}\)) hours.
• D. 6(\(\frac{5}{7}\)) hours.
• E. 5(\(\frac{2}{3}\)) hours.

Answer 1

The Correct Option is C

Let the number of hours taken by Siddharth to complete the task = S
Work done by Siddharth in 1 hour = (\(\frac{1}{S}\))
Let the number of hours taken by Nikita to complete the task = N
Work done by Nikita in 1 hour = (\(\frac{1}{N}\))
Let the number of hours taken by Vinay to complete the task = V
Work done by Vinay in 1 hour = (\(\frac{1}{V}\))
Let the number of hours taken by Neha to complete the task = T
Work done by Neha in 1 hour = (\(\frac{1}{T}\))
Siddharth, Nikita and Vinay take 6 hours 40 minutes to complete the task
= 6 (\(\frac{40}{60}\))
= \(\frac{20}{3}\) hrs
Work done by Siddharth, Nikita and Vinay in 1 hour = 3/20
(\(\frac{1}{S}\)) + (\(\frac{1}{N}\)) + (\(\frac{1}{V}\)) = (\(\frac{3}{20}\)).............................................. (1)
Nikita, Vinay and Neha take 8 hours to complete the task
Work done by Nikita, Vinay and Neha in 1 hour = 1/8
(\(\frac{1}{V}\)) + (\(\frac{1}{V}\)) + (\(\frac{1}{T}\)) = (\(\frac{1}{8}\)).............................................. (2)
Subtracting (2) from (1) we get
(\(\frac{1}{S}\)) - (\(\frac{1}{T}\)) = (\(\frac{3}{20}\)) - (\(\frac{1}{8}\))
(\(\frac{1}{S}\)) - (\(\frac{1}{T}\)) = (\(\frac{1}{40}\))................................. (3)
Also, Siddharth and Neha take 13 hours 20 minutes to complete the task
= 13 (\(\frac{20}{60}\)) = (\(\frac{40}{3}\)) hours
Work done by Siddharth and Neha in 1 hour = (3/40)
(\(\frac{1}{S}\)) + (\(\frac{1}{T}\)) = (\(\frac{3}{40}\)).................................. (4)
Adding (3) and (4) we get
2 x (\(\frac{1}{S}\)) = (\(\frac{4}{40}\))
(\(\frac{1}{S}\)) = \(\frac{1}{20}\)
Substituting in equation 4 we get
(\(\frac{1}{T}\)) = (\(\frac{3}{40}\)) - (\(\frac{1}{20}\)) = (\(\frac{1}{40}\))
Total work done by all four persons together = (\(\frac{1}{S}\)) + (\(\frac{1}{N}\)) + (\(\frac{1}{V}\)) +(\(\frac{1}{T}\))
= (\(\frac{3}{20}\)) + (\(\frac{1}{40}\)) = (\(\frac{7}{40}\))
Total number of hours required = (\(\frac{40}{7}\)) = 5 (\(\frac{5}{7}\)) hours.