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. (A)12 days (B) 12 ½ Days (C) 13 days (D) 15days

Answer 1

Answer:

A

Step-by-step explanation:

so, lets assume b completes work in x days

and a takes x - 6 days

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

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

(2x - 6 / x^2 - 6x ) = 1/4

8x - 24 = x^2 -6x

x^2 -14x + 24 = 0

solving we get x = 12 and 2

so from the given options A is the solution

Answer 2

$\bf{\underline{Given}}:-$

• 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.

$\bf{\underline{To\:Find}}:-$

• The time taken by B to finish the work

$\bf{\underline{Solution}}:-$

Let B alone takes x day to finish the work

and A alone can finish it in ( x - 6) days.

B's 1 day's work = $\rm\dfrac{1}{x}$

A's 1 day's work = $\rm\dfrac{1}{(x-6)}$

(A + B)'s 1 day's work = $\rm\dfrac{1}{4}$

✫ According to the question,

$\rm\:\dfrac{1}{x}+\dfrac{1}{(x-6)}=\dfrac{1}{4}$

$\rm\longrightarrow\:\dfrac{x-6+x}{x(x-6)}=\dfrac{1}{4}$

$\rm\longrightarrow\:4(x-6+x)=x(x-6)$

$\rm\longrightarrow\:4x-24+4x={x}^{2}-6x$

$\rm\longrightarrow\:8x-24={x}^{2}-6x$

$\rm\longrightarrow\:{x}^{2}-14x+24=0$

$\rm\longrightarrow\:{x}^{2}-12x-2x+24=0$

$\rm\longrightarrow\:x(x-12)-2(x-12)=0$

$\rm\longrightarrow\:(x-12)(x-2)=0$

Now,

$\rm\:x-12=0$

$\rm\longrightarrow\:x=0+12$

$\rm\longrightarrow\:x=12$

Then,

$\rm\:x-2=0$

$\rm\longrightarrow\:x=0+2$

$\rm\longrightarrow\:x=2$

∴ Here x cannot be less then 6 so, x = 12

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

So, Option (A) 12 days is correct answer.