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A can do a certain piece of work in 8 days, B can do the same work in 18 days and C an do the same work in 12 days. Find the number of days it will ta
Question

A can do a certain piece of work in 8 days, B can do the same work in 18 days and C an do the same work in 12 days. Find the number of days it will take to complete the same work, if they all work together.

A.

1948\frac{19}{48}​​

B.

7219\frac{72}{19}​​

C.

4819\frac{48}{19}​​

D.

1972\frac{19}{72}​​

Correct option is B

Given:

A can do the work in 8 days.

B can do the work in 18 days.

C can do the work in 12 days.

Solution: 

Total rate of work = 
18+118+112\frac18+\frac1{18}+\frac1{12} 

To find the common denominator, LCM of 8, 18, and 12 = 72 

Total rate of work = 972+472+672=1972\frac9{72}+\frac4{72}+ \frac6{72}= \frac{19}{72}

Total time taken = 7219\frac{72}{19} days

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