Question

LEVEL-1
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.
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Answer 1

Answer:

30 days

Step-by-step explanation:

Let the time taken by B to finish the work alone be = x days

Thus, B’s 1 day work = 1/x

A alone can finish the work in = x - 10

Thus, A’s 1 days work= 1/(x-10)

A and B together can finish the work =  12 days.

Thus, (A and B)'s 1 day work = 1/12

A’s 1 days work + B’s 1 days work = 1/x +  1/(x-10)

Thus, using the equation -

= 1/x +  1/(x-10) = 1/12

= (x-10) + x / 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) = 0  or  (x-4)= 0

x = 30  or  x= 4

Since, the value of x cannot be less than 10, so x= 30

Thus, the time taken by B to finish the work in 30 days.