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Select the correct alternative from the given choices. Tap A can fill a cistern in 12 hours and tap B can fill the same cistern in 8 hours while tap C can empty full cistern in 10 hours. Tap A started at 9 a.m. and tap B started at 11 a.m. At what time tap C should be started such that the cistern will be half full at 1 pm?

Select the correct alternative from the given choices. Tap A can fill a cistern in 12 hours and tap B can fill the same cistern in 8 hours while tap C can empty full cistern in 10 hours. Tap A started at 9 a.m. and tap B started at 11 a.m. At what time tap C should be started such that the cistern will be half full at 1 pm? Correct Answer 12:10 pm

Let the capacity of the cistern be 120 litres (LCM of 12, 8 and 10)

Then, in one-hour A fill 10 litres, B fill 15 litres and C empties 12 litres.

Till 1 pm, A filled for four hours and B filled for two hours.

⇒ A filled (4 × 10) = 40 litres

⇒ B filled (2 × 15) = 30 litres

i.e. (40 + 30) = 70 litres filled by 1 pm.

⇒ C should have emptied 10 litres by 1 pm so that the cistern remains half full.

⇒ C will empty 10 litres in 50 minutes

∴ C should be started at 12:10 pm. 

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