Question

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

Answer 1

Answer:

let the time taken by B =x

so, time taken by A is = x-6

A.T.Q

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

x-6+x/x²-6x=1/4

4(2x-6)= x²-6x

8x-24=x²-6x

x²-6x-8x+24=0

x²-14x+24=0

x²-(12+2)x+24=0

x²-12x-2x+24=0

x(x-12)-2(x-12)=0

(x-12) (x-2)=0

x=12,2

Hope this helps you

Answer 2

12 days

Step-by-step explanation:

Given:

A takes 6 days less than time taken by B to finish a work.

A and B together can finish the work in 4 days.

To find:

Time taken by B to finish the work.

Solution:

This question is related to Time and work.

Let, B can finish the work in x days.

Therefore, A can finish the work in (x - 6) days.

According to question,

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

Either, x - 2 = 0 ⟹ x = 2 [Not possible]

Or, x - 12 = 0 ⟹ x = 12

Therefore, B can finish the work in 12 days.