Question

A takes 6 days less than B
than B to finish
the work. If A and B working together can do it in
in 4 days, how many days B will take to finish the do it Work ?
​

Answer 1

$\sf\large\underline{Let:}$

$\tt{\implies Time\: taken\:by\:B=x}$

$\tt{\implies Time\: taken\:by\:A=x-6}$

$\sf\large\underline{Given:}$

$\tt{\implies Time\: taken\:by\:A+B=4\:days}$

$\sf\large\underline{To\: Find:}$

$\tt{\implies Time\: taken\:by\:B=?}$

$\sf\large\underline{Solution:}$

$\tt{\implies Let,\:A's\:one\:day\: work=\frac{1}{x-6}}$

$\tt{\implies Let,\:B's\:one\:day\: work=\frac{1}{x}}$

$\tt{\implies Let,\:(A+B)'s\:one\:day\: work=\frac{1}{4}}$

$\sf\small\underline{According\:to\: above\: information:}$

$\tt{\implies A's\: work+B's\: work=\dfrac{1}{4}}$

$\tt{\implies \dfrac{1}{x-6}+\dfrac{1}{x}=\dfrac{1}{4}}$

$\tt{\implies \dfrac{x+x-6}{x(x-6)}=\dfrac{1}{4}}$

$\tt{\implies \dfrac{2x-6}{x^2-6x}=\dfrac{1}{4}}$

$\tt{\implies x^2-6x=8x-24}$

$\tt{\implies x^2-6x-8x+24=0}$

$\tt{\implies x^2-14x+24=0}$

• Here, splitting the middle term]

$\tt{\implies x^2-12x-2x+24=0}$

$\tt{\implies x(x-12)-2(x-12)=0}$

$\tt{\implies (x-12)(x-2)=0}$

$\tt{\implies \therefore\:x=12\:and\:2}$

• Here we take any value of x because both values are positive so, we take x=12]

$\sf\large{Hence,}$

$\tt{\implies B\: can\: finish\:the\: work\:in\:12\:days}$

Answer 2

$\bf\large{\underline{\underline{Question:-}}}$

A takes 6 days less than B

than B to finish

the work. If A and B working together can do it in

in 4 days, how many days B will take to finish the do it Work ?

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

• Let B takes x days to finish work

Then,

Number of days taken be A = x-6

Given,

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

Now,

A's one day work =$\sf \frac{1}{x-6}$

B's one day work = $\sf \frac{1}{x}$

† According to question †

We have,

$\sf→ \frac{1}{x-6}+\frac{1}{x}=\frac{1}{4}\\\sf→ \frac{x+x-6}{x(x-6)}=\frac{1}{4}\\\sf→ \frac{2x-6}{x^2-6x}=\frac{1}{4}\\\sf→ 4(2x-6)=x^2-6x\\\sf→ 8x-24=x^2-6x\\\sf→ x^2-6x-8x+24=0\\\sf→x^2-14x+24=0\\\sf→ x^2-12x-2x+24=0\\\sf→ x(x-12)-2(x-12)=0\\\sf→ (x-12)(x-2)=0$

◆ x-2=0 , x=2

◆ x-12=0 , x = 12

Therefore

if we neglected x=2

★ then B will complete the work in 12 days

Either

we neglect x=12

★ B will take 2 days to finish the work.