Two taps can fill a tank in 20 minutes and 30 minutes respectively. There is an outlet tap at exactly half level of that rectangular tank w…

Let the two taps be tap 1 and tap 2 respectively.

Part of tank filled by tap 1 in one minute = 1/20

Part of tank filled by tap 2 in one minute = 1/30

Part of tank filled by both taps in one minute = (1/30) + (1/20) = 1/12

Time taken to fill the tank by both taps without any outlet = 1/(1/12) = 12 min

Note that the outlet is at half the height of tank, so once half the tank is filled, the outlet will start functioning.

Time taken to fill half the tank by tap 1 and tap 2 = 12/2 = 6 min

Time taken to fill the remaining half of the tank when the outlet tap is opened = 24 – 6 = 18 min

Let’s assume that the capacity of half the tank is X litres.

$(\therefore \frac{X}{{10}}\; + \;\frac{X}{{15}} - 248 = \frac{X}{{18}})$

⇒ X/9 = 248

⇒ X = 248 × 9

∴ Volume of full tank = 2 × 248 × 9 = 4464 litres