Question

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:

Step-by-step explanation:

Let B alone finish the work =xdays.

And A alone finish the work =(x−10)days

A' s one day work =   1/(x-10)

 

B's one day work = 1/x

​As it given that

(A+B)  can finish work in 12 days

∴(A+B) one day work=  1/12

⇒A ′ s one day work +B  ′ s one day work=1/12

​⇒  1/x−10  +  1/x =  1/12

 ⇒x+x−10 /  x(x−10) =  1/12

 ⇒  2x−10 /  x(x−10) =  1/12

 ⇒12(2x−10)=x(x−10)

⇒24x−120=x  ^2  −10x

⇒x  ^2  −10x−24x+120=0

⇒x  ^2  −34x+120=0

⇒x  ^2  −30x−4x+120=0

⇒x(x−30)−4(x−30)=0

⇒(x−4)(x−30)=0

⇒x=4or x=30

∵if x =4 then A alone can finish the working=(4−10)=−6dayswhichisnotpossible

∴x=30days

B alone can finish work in 30 days