Question

A B and C working together can finish a piece of work in 4 hours.A alone can do it in 12 hours and B alone can do it in 10 hours.In how many hours will C alone do the same work​

Answer 1

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Answer 2

Answer:

⇒ C can complete the total work in 15 hrs

Step-by-step explanation:

Given data

A, B and C together can finish a work in 4 hours

A alone can do it in 12 hours

B alone can do it in 10 hours

here we need to find how many hours will C take to complete the same work

from given data A can complete the work in 12 hours

⇒ the work can be done by A in 1 hr  = $\frac{1}{12 }$  

B can complete the work in 10 hrs

⇒ the work can be done by B in 1 hr = $\frac{1}{10}$  

lets consider that C can complete the work in x hrs

⇒ the work can be done by C in 1 hr = $\frac{1}{x}$  

the work can be done by A, B and C in 1 hr = 1/4 which will be equals to the sum of works done by A,B and C in 1 hr

        ⇒  $\frac{1}{12} + \frac{1}{10} + \frac{1}{x} = \frac{1}{4}$  

        ⇒  $\frac{5+ 6 }{60} + \frac{1}{x} = \frac{1}{4}$

        ⇒  $\frac{11}{60} + \frac{1}{x} = \frac{1}{4}$

        ⇒  $\frac{11x+ 60}{60x} = \frac{1}{4}$  

        ⇒ 44x + 240 = 60x

        ⇒  16x = 240

        ⇒   x = 240/ 16 = 15 hrs  

⇒ C can complete the total work in 15 hrs.