Question

A and B can do a piece of work in 10 hours,B and C in 12 hours and C and A in 15 hours.How long will they take if they work together?How long will each take to complete the work independently​

Answer 1

please see the attachment

Answer 2

A , B , C can complete the work in 8 hours working together

A alone can complete the work in 24 hours

B alone can complete the work in 120/7 hour

C alone can complete the work in 40 hours

Solution:

From given,

A and B can do a piece of work in 1 hour = $\frac{1}{10}$

$A + B = \frac{1}{10}$

B and C can do a piece of work in 1 hour = $\frac{1}{12}$

$B + C = \frac{1}{12}$

C and A can do a piece of work in 1 hour =  $\frac{1}{15}$

$C + A = \frac{1}{15}$

Therefore,

$A + B + B + C + C + A = \frac{1}{10} + \frac{1}{12} + \frrac{1}{15}\\\\2(A + B + C) = \frac{1}{4}\\\\A + B + C = \frac{1}{8}$

Thus,

A , B, C can do in 1 hour = $\frac{1}{8}$

Thus,

A , B , C can complete the work in 8 hours

$\frac{1}{10} + C = \frac{1}{8}\\\\C = \frac{1}{40}$

Thus, C can complete the work in 40 hours

$\frac{1}{15} + B = \frac{1}{8}\\\\B = \frac{7}{120}$

Thus B can complete the work in 120/7 hour

$A + \frac{1}{12} = \frac{1}{8}\\\\A = \frac{1}{24}$

Thus A can complete the work in 24 hours

Learn more:

A and B can do a piece of work in 40 days, B and C in 30 days and C and A in 24 days. in what time can each finish it working alone?

https://brainly.in/question/7224836

A and B can do the piece of work in 12 days B and C in 15 days C and a in 20 days if a b c work together they will complete the work in how many days

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