Question

PROBLEMS ON TIME AND WORK AND
54. A takes 10 days less than the time taken by B to finish a piece of work.
If both A and B together can finish the work in 12 days, find the time
taken by B to finish the work.​

Answer 1

Answer:

30 days

Step-by-step explanation:

Let B can alone finish the work = x days

So, A can alone finish the work = (x - 10) days

Now, one day work of A = 1/x−10

and one day work of B = 1/x

Now, given (A + B) can finish the work = 12 day

So, one day work of (A + B) = 112

⇒1/x−10+1/x=1/12

⇒x+x−10/x*(x−10)=1/12

⇒2x−10/x²−10x=1/12

⇒12(2x−10)=x2−10x

⇒24x−120=x²−10x

⇒x²−10x−24x+120=0

⇒x²−34x+120=0

⇒x²−30x−4x+120=0

⇒x(x−30)−4(x−30)=0

⇒(x−30)*(x−4)=0

⇒x=30,4

if x = 4, then A alone can finish the work = 4 - 10 = -6, which is not possible.

So, x = 30

Hence, B can alone finish the work = 30 days

Hope you got it !

Answer 2

Step-by-step explanation:

I hope this can help u...