Question

15. Two taps A and B together fill a swimming pool
in 15 hours. Taps A and Bare kept open for
12 hours and then tap B is closed. It takes
another 8 hours for the swimming pool to be
filled. How many hours does each tap require to
fill the swimming pool?​

Answer 1

✪ Question :-

❦ Two taps A and B together fill a swimming pool

in 15 hours. Taps A and Bare kept open for

12 hours and then tap B is closed. It takes

another 8 hours for the swimming pool to be

filled. How many hours does each tap require to

fill the swimming pool ?

✰ Solution :-

it is given that, Both Tap A and B can will the pool in 15 hours .

That means , we can say that,

➺ (A + B) = 1/15 . ( per hour they fill ).

Now, Both are opened for 12 hours and than B is closed , that means Rest was filled by A alone in 8 more hours .

So,

⟿ 12(A+B) + 8A = 1 ( Total )

Putting value of (A+B) here , we get,

⟿ 12 * (1/15) + 8A = 1

⟿ 4/5 + 8A = 1

⟿ 8A = 1 - 4/5

⟿ 8A = 1/5

⟿ A = 1/(5*8)

⟿ A = 1/40.

So, A will Fill alone the swimming pool in 40 hours.

____________________________________

Now, putting This value we get,

➳ A + B = 1/15

➳ 1/40 + B = 1/15

➳ B = 1/15 - 1/40

➳ B = (8 - 3) /120

➳ B = 5/120

➳ B = 1/24

So, A will Fill alone the swimming pool in 24 hours.

_____________

Answer 2

$\huge\mathbb{SOLUTION:-}$

Given:-

.Tap A and B can fill the swimming pool in 15hrs

Means both tap and fill 1/15 of pool in 1 hrs

• So (A+B) = 1/15(in 1hrs) ........(i)

$\bf\underline{\red{According \:To\: Question}}$

It is give. that 12(A+B)+8A Fills the swimming pool complete

$\sf\implies 12(A+B)+8A=1\\ \\ \sf\bullet \:\:\:(A+B)=\dfrac{1}{15}\\ \\ \sf\implies 12\times \dfrac{1}{15}+8A=1\\ \\ \sf\implies 8A=1-\dfrac{12}{15}\\ \\ \sf\implies 8A=\dfrac{15-12}{15}\\ \\ \sf\implies A=\dfrac{\cancel3}{\cancel{15}}\times \dfrac{1}{8}\\ \\ \sf\implies A=\dfrac{1}{40}$

• Tap A alone can fill the pool in 40hrs

Now Tap B

According to our equation (i)

Put the value of tap A in eq.1

$\sf\implies (A+B)=\dfrac{1}{15}\\ \\ \sf\implies \dfrac{1}{40}+B=\dfrac{1}{15}\\ \\ \sf\implies \dfrac{1+40B}{40}=\dfrac{1}{15}\\ \\ \sf\implies 1+40B= \dfrac{40}{15}\\ \\ \sf\implies 40B\:\:=\dfrac{40-15}{15} \\ \\ \sf\implies 40B\:\:=\dfrac{25}{15}\\ \\ \sf\implies \:B\:\:=\dfrac{25}{15}\times \dfrac{1}{40}\\ \\ \sf\implies B=\cancel{\dfrac{25}{600}}\\ \\ \sf\implies B=\dfrac{1}{24}$

• TapB alone fill the swimming pool in 24 hrs

$\boxed{\sf{tap\:A\: requires\:40hrs}}$

$\boxed{\sf{tap\:B\: requires\:24hrs}}$