Question

A takes 6 days less than the time taken by b to finish a piece of work. If both a and b together can finish it in 4 days find the time taken by b to finish the work alone.

Answer 1

Solution :

Given :
Let the time taken by B to finish the work alone be x days
So, A can complete it in (x - 6) days.
B's one day work = 1/x
A's one day work = 1/(x - 6)

A and B together can finish it in 4 days.
(A + B)'s one day work = 1/4


According to the question,


$= > \frac{1}{x} + \frac{1}{x - 6} = \frac{1}{4} \\ \\ = > \frac{x - 6 + x}{x(x - 6)} = \frac{1}{4} \\ \\ = > 4(x - 6 + x) = x(x - 6) \\ \\ = > 4x - 24 + 4x = {x}^{2} - 6x \\ \\ = > {x}^{2} - 8x - 6x + 24 = 0 \\ \\ = > {x}^{2} - 12x - 2x + 24 = 0 \\ \\ = > x(x - 12) - 2(x - 12) = 0 \\ \\ = (x - 2)(x - 12) = 0 \\ \\ = > x = 2 \: \: \: \: or \: \: \: x = 12$


B finished work alone = x = 2 days
A finished it in (x - 6) = 2 - 6 = - 4 days.
So, x ≠ 2 (Because Time can't be negative)


Hence,
The time taken by B to finish the work alone = 12 days.

Answer 2

Answer:

no. of days taken by A to finish that work = x

then, no. of days taken by B to finish that work = x+6

now, work done by A in one day = 1/x and work done by B in one day = 1/x+6

now, work done by both A and B in one day,

1/x + 1/x+6 = 1/4

{(x+6)+x}/x(x+6) = 1/4

8x + 24 = x2 + 6x

x2-2x - 24 = 0

x2 -6x +4x -24 = 0

x(x-6) +4(x-6) = 0

(x+4) (x-6) = 0

so, x= 6  (neglecting x = -4)

so, time taken by B to finish the work = x+6 = 12 days