Two taps, A and B are turned on to fill a tank of volume 500 l .tank A can fill 0.5 l per second and tank B can fill 1 l per second . they are turned on for 20 seconds and third tap C is also turned on. Now, the the tank completely fills in 94 seconds . Find how much water tap C can fill in a second
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To find :
how much does tap C fills water in 1 second
Given :
Solution :
Given, Tap A and B is turned on for 20 seconds
hence,
total water filled = 20(1+0.5)l
[tex]\longrightarrow \bold{total \: water \: filled \: = 20(1.5)l} \\ \longrightarrow \bold{total \: water \: filled \: = } \boxed{ \bold{30 \: litre}}[/tex]
hence, volume remaining :
500 - 30 litres
[tex] \boxed{ \bold{ \red{ 470 \: litres}}}[/tex]
[tex] \boxed{ \bold{ \blue{let \: the \: rate \: of \: tap \: C \: is \: x}}}[/tex]
so, time taken to fill remaining tank = 94 seconds
[tex]\longrightarrow \bold{ \frac{470}{a + b + c} = 94 \: s } \\ \\ \longrightarrow \bold{ \frac{a + b + c}{470} = \frac{1}{94} } \\ \\ \longrightarrow \bold{a + b + c = \frac{470}{94} } \\ \longrightarrow \boxed{ \bold{a + b + c = 5 \: }}[/tex]
hence, A+B+C = 5 l/s
[tex]\longrightarrow \bold{0.5 + 1 + c = 5} \\ \longrightarrow \bold{1.5 + c = 5 \: litre} \\ \longrightarrow \bold{c = 5 - 1.5 \: litre} \\ \longrightarrow \boxed{ \bold{c = 3.5 \: litre \: ps }}[/tex]
hence, Rate of C = 3.5 l/s
hence, tap C can fill 3.5 litre in a second
To find :
how much does tap C fills water in 1 second
Given :
rate of tap A = 0.5 l/s
rate of tap B = 1 l/s
volume of tank = 500 l
Solution :
Given, Tap A and B is turned on for 20 seconds
hence,
total water filled = 20(1+0.5)l
hence, volume remaining :
500 - 30 litres
so, time taken to fill remaining tank = 94 seconds
hence, A+B+C = 5 l/s
hence, Rate of C = 3.5 l/s
hence, tap C can fill 3.5 litre in a second
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