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, find the time taken by B to finish the work.​

Answer 1

Answer:

A takes 6 days less than B to finish a piece of work.

Time taken by A = x - 6 days

Time taken by B = x days.

If both A and B together can finish the work in 4 days -

$\frac{1}{x - 6} + \frac{1}{x} = \frac{1}{4} \\ \\ \frac{x + x - 6}{x(x - 6)} = \frac{1}{4} \\ \\ \frac{2x - 6}{x(x - 6)} = \frac{1}{4} \\ \\ 8x - 24 = {x}^{2} - 6x$

${x}^{2} - 14x + 24 = 0 \\ \\ {x}^{2} - 12x - 2x + 24 = 0 \\ \\ x(x - 12) - 2(x - 12) = 0 \\ \\ (x - 2)(x - 12) = 0$

Here x cannot be less than 6, so the x = 2 is invalid.

So, the time taken by B to finish the work = 12 days.

Answer 2

Answer:

Step-by-step explanation:

a=x-6

b=x

x+x-6=4

2x-6=4

2x=10

x=5

a takes 1 day whereas b takes 5