Question

TIS. 2
6. 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.
Ans. 12 days​

Answer 1

Answer:

The time taken by B to finish the work = 12 days

Step-by-step explanation:

Given :

• 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

To find :

the time taken by B to finish the work

Solution :

Let the time taken by B to finish the work be x days

Then the time taken by A to finish the same work is

= (x - 6) days

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

Work done by A and B together in one day = 1/4

Work done by A in one day =  $\tt \dfrac{1}{x-6}$

Work done by B in one day =  $\tt \dfrac{1}{x}$

Work done by A and B together in one day = Work done by A in one day + Work done by B in one day

   $\tt \dfrac{1}{4}=\dfrac{1}{x-6}+\dfrac{1}{x} \\\\\\ \tt \dfrac{1}{4}=\dfrac{x+x-6}{(x-6)(x)} \\\\\\ \tt \dfrac{1}{4}=\dfrac{2x-6}{x^2-6x} \\\\\\ \tt x^2-6x=4(2x-6) \\\\ \tt x^2-6x=8x-24 \\\\ \tt x^2-6x-8x+24=0 \\\\ \tt x^2-14x+24=0$

Solving the quadratic equation by factorization,

x² - 14x + 24 = 0

x² - 12x - 2x + 24 = 0

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

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

⇒ x - 12 = 0 ; x = 12

⇒ x - 2 = 0 ; x = 2

If x = 2,

x - 6 = 2 - 6 = -4

Time can not be negative. Hence, x should not be equal to 2.

Therefore, x = 12

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