Question

please answer 2nd question with full explanation​

Answer 1

Answer:

5 minutes, 8 minutes

Step-by-step explanation:

Let the bigger tap takes 'x' minutes to fill the tank.

Then, the smaller tap takes (x + 3) minutes.

(i) Work done by bigger tap in 1 - minute = (1/x).

(ii) Work done by smaller tap in 1 - minute = (1/x + 3).

∴ Time taken by both taps = 13 (1/3) minutes = (40/13) minutes.

Work done by both the taps in 1 - minute = (13/40) minutes.

Now,

⇒ (1/x) + (1/x + 3) = 13/40

⇒ (x + 3 + x)/x(x + 3) = 13/40

⇒ 40(2x + 3) = 13x(x + 3)

⇒ 80x + 120 = 13x² + 39x

⇒ 13x² - 41x - 120 = 0

⇒ 13x² - 65x + 24x - 120 = 0

⇒ 13x(x - 5) + 24(x - 5) = 0

⇒ (x - 5)(13x + 24) = 0

⇒ x = 5, -24/13

⇒ x = 5.

Therefore:

Time taken by bigger tap = 5 minutes.

Time taken by smaller tap = 8 minutes.

Hope it helps!

Answer 2

Let one tap fill the tank in x hrs.

Therefore, other tap fills the tank in (x + 3) hrs.

Work done by both the taps in one hour is

1/x + 1/(x+3) = 13/40

(2x + 3)40 = 13(x2 + 3x)

13x2 – 41x – 120 = 0

(13x + 24)(x – 5) = 0

x = 5 (rejecting the negative value)