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1. A tank is 7 metre long and 4 meter wide wide. At what speed should water run through a pipe 5 cm broad and 4 cm deep so that in 6 hours and 18 minutes water level in the tank rises by 4.5 meter?

A. 10 km/hours

B. 12 km/hours

C. 8 km/hours

D. None of these

Solution:

Rate of flow of water = x cm/minute
∴ Volume of water that flowed in the in 1 minutes
= (5 × 4 × x) = 20 x cu.cm.
∴ Volume of water that flowed in the tank in 6 hours 18 minutes.
i.e. (6 × 60 + 18) = 378 minutes
= 2x × 378 cu. cm.
According to question,

\begin{aligned} 20 x \times 378 = 700 \times 400 \times 450 \\ \Rightarrow x = (\frac{700 \times 400 \times 450}{20 \times 378}) cm /minutes \\ \Rightarrow x = (\frac{700 \times 400 \times 450 \times 60}{100000 \times 20 \times 378}) km/hours \\ \Rightarrow x =  10 km/hours \end{aligned}

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