Question

Question 2:
A and B can do a piece of work in 15 days. B and C can do
the same work in 10 days and A and C can do the same
work in 12 days. Time taken by A, B and C together to do
the job is? A और B 15 दिनों में एक काम कर सकते है। B और C एक ही
काम को 10 दिन और A और C एक ही काम को 12 दिनों में कर सकता है।
काम करने के लिए A, B और C द्वारा एक साथ लिया गया समय है?​

Answer 1

Answer: it would take A 40 days to do the job by himself.

Step-by-step explanation:

Let  a  be A’s work rate,  b  be B’s work rate and  c  be C’s work rate.

If A and B take 15 days to do a job then together, their rate is  115  jobs/day.

So  a+b=115  jobs/day.

Similarly, A, B and C take 8 days to do the same job together.

So  a+b+c=18  jobs/day.

Subtracting,  c=18−115=7120  jobs/day.

If B and C together take  x  days to do the job then their rate is

b+c=1x  jobs/day

A and C take 2 days longer to do the same job so they take  x+2  days. That is a rate of

a+c=1x+2  jobs/day.

Substituting for c and rearranging we get

b=1x−7120

a=1x+2−7120

a+b=1x+2−7120+1x−7120=115

Multiplying both sides of this equation by  60x(x+2)  and rearranging gives

11x2−98x−120=0

or  (x−10)(11x+12)=0

We take the positive  x=10  as our solution.

This means that  b=110−7120=124  jobs/day

and  a=110+2−7120=140  jobs/day.

Therefore, it would take A 40 days to do the job by himself.