Question

A and B can do a piece of work in 22 1/2days. B takes 24 days more than A to finish the work alone. A can finish the whole work in?

Answer 1

let A takes x days to finish the whole work.

Expalaination:
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A 's 1 day's work = 1/ x

B 's 1 day's work = 1/ (x + 24)

(A + B)'s 1 day's work

1/ (22 1/2) = 1/45/2 = 2/ 45

1/ x + (1/ x + 24) = 2/ 45

x + 24 + x = x ( x + 24) × 2 / 45

45 (2x + 24) = 2x^2 + 48x

90x + 1080 = 2x^2 + 48x

2x^2 - 42x - 1080 = 0

2( x^2 - 21x - 540) = 0

x^2 - 21x - 540 = 0

x^2 - 36x + 15x - 540 = 0

x( x - 36) + 15( x - 36) = 0

(x - 36) ( x + 15) = 0

x = 36, - 15

neglec -15 , days can't count as -ve.

so take +ve value of x = 36

Answer:
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A alone can finish the work in 36days