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:

B-6=A

B-6+B= 4

B=4+6=10

So, B take 10days to finish the work .

Answer 2

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

Let assume that

Number of days taken by B = x days

So,

Number of days taken by A = x - 6 days

So,

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

and

$\rm :\longmapsto\:A's \: one \: day \: work \: = \dfrac{1}{x - 6}$

Now,

According to statement,

A and B together can take 4 days to finish the work

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

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

$\rm :\longmapsto\:\dfrac{2x - 6}{(x - 6)x} = \dfrac{1}{4}$

$\rm :\longmapsto\:\dfrac{2x - 6}{ {x}^{2} - 6x} = \dfrac{1}{4}$

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

$\rm :\longmapsto\: {x}^{2} - 6x - 8x + 24 = 0$

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

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

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

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

$\bf\implies \:x = 12 \: \: \: or \: \: \: x = 2 \: \{ \: reject \}$

Hence,

Number of days taken by B = 12 days

and

Number of days taken by B = 6 days

Additional Information

Nature of roots :-

Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

If Discriminant, D > 0, then roots of the equation are real and unequal.

If Discriminant, D = 0, then roots of the equation are real and equal.

If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

Discriminant, D = b² - 4ac