Question

⭐A takes 5days less than the time taken by B to do some work. they can do work together in 6 days. Find the number of days in which each of them can do the work separately.⭐

CLASS 10 CHAPTER :QUADRATIC EQUATIONS

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Answer 1

Let the time taken by B to finish the work be 'x'.

Given that A takes 5 days less than the time taken by B.

Hence, A alone can finish the work in (x - 5) days.

Given that they can do work together in 6 days.

Work done by (A + B) in 1-day = (1/6).

Now,

A's one day work + B's one day work = (A + B)'s one day work.

⇒ (1/x - 5) + (1/x) = 1/6

⇒ 6(x + x - 5) = x(x - 5)

⇒ 6(2x - 5) = x^2 - 5x

⇒ 12x - 30 = x^2 - 5x

⇒ x^2 - 17x + 30 = 0

⇒ x^2 - 2x - 15x + 30 = 0

⇒ x(x - 2) - 15(x - 2) = 0

⇒ (x - 2)(x - 15) = 0

⇒ x = 2,15.

If the times it(B) takes is 2 days, then the time taken by A will be -5, which is not possible.

So, consider x as 15.

Then:

⇒ x - 5

⇒ x = 10.

Therefore:

⇒ A alone can finish the work in 10 days.

⇒ B alone can finish the work in 15 days.

Hope it helps!

Answer 2

Answer:

let the A works done be x.

and B be x+5

Step-by-step explanation:

6(1/x+1/x+5)=1

1/x+1/x+5=1/6

x+x+5/x(x+5)=1/6

6x +6x+30=x^2+5x

-x^2+10x-3x+30

-x(x-10)-3(x-10)

-(x-3)(x-10)

-x=3 &x=10

a =10

b= x+5= 15