Question

Two pipes A and B can fill a tank in 12 and 15 hours respectively and the third pipe C can empty in 20 hours. if in the 1st hour all three pipes are opend and in the second hours only B and C are opend and the 3rd hour only C is opend and the process is repeated again and again then find in how many hours the tank will be filled ?​

Answer 1

${\boxed{\mathtt{\green{Answer}}}}$

➾ The tank will be filled in 45 hours.

${\boxed{\mathtt{\green{GIVEN}}}}$

• A can fill the tank in 12 hours
• B can fill the tank in 15 hours
• C can empty the tank in 20 hours.

${\boxed{\mathtt{\green{To\: Find}}}}$

• In how many hours the tank will be filled.

${\boxed{\mathtt{\green{Solution}}}}$

Firstly let's find the capacity of each for filling the tank in 1 hour.

In 1 hour A can fill = 1/12 th part

In 1 hour B can fill = 1/15 th part

In 1 hour C can empty = 1/20 th part

For finding the capacity of each tap firstly find the LCM of the part they can fill in per hour.

$\implies \: \frac{5 + 4 - 3}{60}$

Hence we go there capacity which is.

Capacity of A = 5 volume

Capacity of B = 4 volume

Capacity of C = 3 volume

In 1st hour , Tank will be filled :-

A + B - C = 5 + 4 - 3

➾ 6 volume

In 2nd hour

B - C = 4 - 3

➾ 1 volume

In 3rd hour

C = - 3

In three hour volume of tank filled :-

➾ 6 + 1 - 3 = 4 volume

In 3 hours 4 out of 60 volume of tank is filled . Then in each volume Will be filled in :-

$\implies \: \frac{3}{4} hours$

Then 60 volume will be filled in :-

$\implies \: \frac{3}{4} \times 60 \: = 45$

Hence answer is 45 hours

Answer 2

In 1 hour A can fill = 1/12 th part

In 1 hour B can fill = 1/15 th part

In 1 hour C can empty = 1/20 th part

Capacity of A = 5 volume

Capacity of B = 4 volume

Capacity of C = 3 volume

In 1st hour , Tank will be filled :-

A + B - C = 5 + 4 - 3

➾ 6 volume

In 2nd hour

B - C = 4 - 3

➾ 1 volume

In 3rd hour

C = - 3

In three hour volume of tank filled :-

➾ 6 + 1 - 3 = 4 volume

In 3 hours 4 out of 60 volume of tank is filled . Then in each volume Will be filled in :-

\begin{lgathered}\implies \: \frac{3}{4} hours\\\end{lgathered}

⟹

4

3

hours

Then 60 volume will be filled in :-

\begin{lgathered}\implies \: \frac{3}{4} \times 60 \: = 45 \\\end{lgathered}

⟹

4

3

×60=45