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A man can do a job in 15 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all wo
Question

A man can do a job in 15 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together ?

A.

less than 6 days

B.

exactly 6 days

C.

approximately 6.4 days

D.

7 days

Correct option is C

Given:
Time taken by man = 15 days
Time taken by father = 20 days
Time taken by son = 25 days
Formula Used:
Total Work = L.C.M. of time taken
Efficiency = TotalWorkTimeTaken \frac{Total Work}{Time Taken}​​
Solution:
Find the total work by taking the L.C.M. of 15, 20, and 25.
Total Work = 300 units
Calculate the efficiency of each person:
Man's efficiency = 30015\frac{300}{15}​ = 20 units/day

Father's efficiency =30020 \frac{300}{20}​ = 15 units/day

Son's efficiency = 30025 \frac{300}{25}​ = 12 units/day
Total efficiency when working together:
Total Efficiency = 20 + 15 + 12 = 47 units/day
Time taken together = Total WorkTotal Efficiency \frac{Total\ Work}{Total\ Efficiency}​​
Time taken = 30047\frac{300}{47}​​
Time taken = 6.38 days
This value is approximately 6.4 days.
Final Answer
So the correct answer is (c)

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