Question

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

Answer 1

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

$\longrightarrow \bold{total \: water \: filled \: = 20(1.5)l} \\ \longrightarrow \bold{total \: water \: filled \: = } \boxed{ \bold{30 \: litre}}$

hence, volume remaining :

500 - 30 litres

$\boxed{ \bold{ \red{ 470 \: litres}}}$

$\boxed{ \bold{ \blue{let \: the \: rate \: of \: tap \: C \: is \: x}}}$

so, time taken to fill remaining tank = 94 seconds

$\longrightarrow \bold{ \frac{470}{a + b + c} = 94 \: s } \\ \\ \longrightarrow \bold{ \frac{a + b + c}{470} = \frac{1}{94} } \\ \\ \longrightarrow \bold{a + b + c = \frac{470}{94} } \\ \longrightarrow \boxed{ \bold{a + b + c = 5 \: }}$

hence, A+B+C = 5 l/s

$\longrightarrow \bold{0.5 + 1 + c = 5} \\ \longrightarrow \bold{1.5 + c = 5 \: litre} \\ \longrightarrow \bold{c = 5 - 1.5 \: litre} \\ \longrightarrow \boxed{ \bold{c = 3.5 \: litre \: ps }}$

hence, Rate of C = 3.5 l/s

hence, tap C can fill 3.5 litre in a second

Answer 2

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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