Question

A takes 6 days less than B to finish a piece of work. If both A and B together can finish the work in 4 days, then find the time taken by B to finish the work.
(Class 10 Maths Sample Question Paper)

Answer 1

Let's B alone takes x days to finish the work and A alone can finish the work in (x-6) days.

B's one day work = 1/x
A’s one day work = 1/(x-6)

A’s one day work +B’s one day work =1/x+1/(x-6)..................(1)

ATQ

1 day work of A and B together= ¼……….(2)

From Equation 1 and 2
1/x+1/(x-6) = ¼

x - 6 +x / x(x-6) = ¼
(2x -6) × 4= x(x-6)
8x -24  = x² -6x
x² -6x -8x +24 = 0
x² -14x +24 = 0
x² -12x -2x +24 = 0
x(x -12) - 2(x -12)= 0
(x-2) (x-12)=0
(x-2)= 0 or  (x-12)=0
x = 2 or x = 12

But x cannot be less than 6
So , x= 12

Hence, B alone can finish the work in 12 days.

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