Question

There are 4 filling pipes and 3 emptying pipes capable of filling in 12 mins and emptying in 15 min. if all the pipes are opened together and as a result they ill 10 ltrs of water per minute, find the capacity of the tank.

Answer 1

Gɪᴠᴇɴ :-

• A Filling Pipe Total Time to Fill = 12 Mins.
• A Emptying Pipe Total Time to Empty = 15 Mins.
• Total Filling Pipes = 4
• Total Empty Pipes = 3 .

Tᴏ Fɪɴᴅ :-

• Capacity of Tank ?

Sᴏʟᴜᴛɪᴏɴ :-

→ LCM of 12 & 15 = 60 units = Let Total Capacity of Tank .

So,

→ Efficiency of a Filling Pipe = (Capacity/Total Time taken) = (60/12) = 5 units/min.

→ Efficiency of 4 such Filling Pipes = 5*4 = 20 units/min.

Similarly,

→ Efficiency of a Emptying Pipe = (Capacity/Total Time taken) = (60/15) = 4 units/min.

→ Efficiency of 3 such Emptying Pipes = 4*3 = 12 units/min.

Hence,

→ Efficiency of 4 filling pipes and 3 emptying pipes = 20 - 12 = 8 units/min.

_________

now we have given That, if all the pipes are opened together and as a result they ill 10 ltrs of water per minute.

Therefore ,

→ 8 units --------- 10Ltrs.

→ 1 units --------- (10/8)Ltrs.

→ 60 units(Total tank capacity) -------- (10/8) * 60 = 75 Ltrs. (Ans).

Hence, Total capacity of the Tank is 75 Litres.

____________________

Short :-

Let us Assume That , 4 filling pipes and 3 emptying pipes can fill the tank full in x Minutes.

So,

→ x[ 4/12 - 3/15 ] = 1

→ x[ 1/3 - 1/5 ] = 1

→ x[ (5 - 3)/15 ] = 1

→ x(2/15) = 1

→ x = (15/2) Minutes.

Hence,

→ Capacity of Tank = (15/2) * 10 = 75 Litres. (Ans).

_____________________

Note :- if Time of 4 filling pipes together is given 15min. to fill & 3 emptyping pipes total time to empty is given as 12 mins.

Than :-

→ 4 Filling pipes Fill than tank in = 12 min.

→ per min. Efficiency of 4 filling pipes = (1/12)

Similarly,

→ 3 Emptying pipes Empty than tank in = 15 min.

→ per min. Efficiency of 3 Emptying pipes = (1/15)

Therefore,

→ Per min. All Together fill the tank = (1/12 - 1/15) .

Now , Let us Assume That, Total Time Taken to fill the empty tank is x mins.

So,

→ x[ 1/12 - 1/15 ] = 1

→ x[ (5 - 4)/60 ] = 1

→ x(1/60) = 1

→ x = 60 Minutes.

Hence,

→ Capacity of Tank = 60 * 10 = 600 Litres. (Ans).

___________________

Answer 2

GIVEN :-

♦ Number of filling pipes = 4

♦ Number of emptying pipes = 3

♦ Time taken by the filling pipes to fill = 12 mins

♦ Time taken by the emptying pipes to empty = 15 mins

♦ If all pipes are opened together, capacity filled by them per minute = 10 litres

TO FIND :-

The capacity of the tank.

SOLUTION :-

Let the total time taken by all the pipes to fill the tank be x.

Time taken by 1 filling pipe to fill the tank = 1/12 mins

Time taken by 4 filling pipes to fill the tank = 4/12 = 1/3 mins

$\rule{100}{2}$

Time taken by 1 emptying pipe to empty the tank = 1/15 mins

Time taken by 3 emptying pipes to empty the tank = 3/15 = 1/5 mins

$\rule{100}{2}$

We get that,

x × (1/3 - 1/5) = 1

⇒x × (5-3)/15 = 1

⇒x × 2/15 = 1

⇒x = 15/2

⇒x = 7.5 mins

$\rule{100}{2}$

A/q, the pipes fill 10 litres per minute.

So, amount filled in 7.5 mins = 10 * 7.5

= 75 litres

$\rule{100}{2}$

∴ Thus, the capacity of the tank is 75 litres.