A pipe can fill a tank in 0.9 hours and another pipe can empty in 0.7 hours. If tank is completely filled and both pipes are opened simultaneously then 450 liters of water is removed from the tank in 2.5 hours. What is the capacity of the tank? (Pipe & Cistern)

Shohan

6 views

2025-01-04 04:42

1 Answers

Shohan

Here, 0.9 hours = 0.9 * 60 = 54 minutes; 0.7 hours = 0.7 x 60=42 minutes

2.5 hours = 2.5 x 60 = 150 minutes

In 54 minutes first pipe can fill= $\frac{150}{54} = \frac{25}{9} p a r t o f t h e \tan k$

And in 42 minutes another pipe can empty = $\frac{150}{42}$ = $\frac{25}{7}$ part of the tank

As, the tank was filled, after opening both the tank will be filled to

$= 1 + \frac{25}{9} - \frac{25}{7} = \frac{63 + 175 - 225}{63} = \frac{238 - 225}{63} = \frac{13}{63} p a r t ∴ E m p t y p a r t = 1 - \frac{13}{63} = \frac{63 - 13}{63} = \frac{50}{63}$

According to question

$\frac{50}{63}$ parts of tank = 450 liters

$∴ 1 o r f u l l p a r t o f \tan k = \frac{450 \times 63}{50} = 567 l i t e r s .$

6 views Answered 2024-12-14 13:31

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