With both inlets open, a water tank will be filled with water in 48 minutes. The first inlet alone would fill the tank in 2 hours. What is the capacity of the tank, in cubic meters, if in every minute the second inlet admits 50 cubic meters of water more than the first?

A. 9,000
B. 10,500
C. 11,750
D. 12,000
E. 13,000
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Both inlets fill the tank in 48 mins

Inlet one can fill the tank in 2 hrs = 120 mins

inlet two can fill the tank in x mins

1/120 + 1/ x = 1/48
1/x = 1/48 - 1/120 = (5-2)/240 = 3/240 = 1/80

Inlet two can fill the tank in 80 mins

If both inlets opened for 120 mins then
Inlet one will fill full tank capacity
Inlet two will fill 1.5 times capacity of the tank. ---(1)

In every minute inlet two adds 50 cubic meters more than inlet one
In 120 mins inlet two adds 50*120 = 6000 cubic meters more than inlet one.---(2)

From (1) and (2)

Half the capacity of tank is 6000 cubic meters

The capacity of the tank is 12000 cubic meters

Ans d
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Hello Madam,


I have a doubt..... is this equation correct :

Assuming C as capacity
A as time taken by inlet 1 to fill the tank
B as time taken by inlet 2 to fill the tank.

\((\frac{C}{A}+\frac{C}{B})48=C\).........Is this correct ??
We know that inlet 1 takes 2hr or 120 mins to fill the tank

\((\frac{C}{120}+\frac{C}{B})48=C\)
Then

\((\frac{1}{120}+\frac{1}{B})48=1\)
B=80

I am taking C in the equation for better understanding and because as the rate is not given purely in terms of time taken , as a safer approach I used C.

Also madam as \(\frac{1}{80}-\frac{1}{120}=\frac{1}{240}\)

Can I say 1/240 is the rate difference between the two inlets and (1/240)1 = 50

i.e here 1/240 is the rate, time = 1 and 50 is work done.

Thanks

Correct.



This is correct though you should know how you obtained it.
1/80 is the rate and its units are 1/80 of the tank per minute. Since you are using C for capacity, this could also be written as C/80 cubic meters/minute.

So C/80 - C/120 = C/240 cubic meters/minute



1/240 of the tank per minute is the rate difference. In capacity terms, C/240 is the rate difference.

(C/240) cubic meters/minute * 1 minute = 50 cubic meters

C = 240*50 = 12000 cubic meters
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pipe 2 takes 80 min to fill the tank, pipe 1 - 120 min - which corresponds to +50% produtivity of pipe 2. we are given that this extra productivity denotes 50 cubic meters per min more than pipe 1 pumps. hence this proportion can be possible only if pipe 1 pumps 100 cm and pipe 2 then pumps 150 cm.

(100 + 150) * 48 = 12 000
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First fills in 120 minutes

Together in 48 minutes, then second one fills in 80 minutes. ( 1/120 + 1/second one= 1/48 )

Let first fills x cubic meter per second then second fills (x+50) cubic meter per second

Tank capacity for first = Tank capacity for second
120 * x = 80 * (x + 50)

Solve x =100, i.e first fills at 100 and second at 150 cubic meter per minute

So tank capacity = 120 * 100 or 80*150 = 12,000

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