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Three taps A, B and C together can fill an empty cistern in 10 minutes. The tap A alone can fill it in 30 minutes and the tap B alone in 40 minutes. How long will the tap C alone take to fill it?

Correct Answer: 24 minutes
A, B and C together can fill 100% empty tank in 10 minutesWork rate of (A + B + C) = $$\frac{{100}}{{10}}$$ = 10% per minuteA alone can fill the tank in 30 minutesWork rate of A = $$\frac{{100}}{{30}}$$ = 3.33% per minuteB alone can fill the tank in 40 minutesWork rate of B = $$\frac{{100}}{{40}}$$ = 2.5%Work rate of (A + B) = 3.33 + 2.5 = 5.83% per minuteWork rate of C, = Work rate of (A + B + C) - (A + B)= 10 - 5.83 = 4.17% per minuteSo, C takes = $$\frac{{100}}{{4.17}}$$ ≈ 24 minutes to fill the tank

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In a public bathroom there are n taps 1,2,3...n. Tap1 and Tap2 take equal time to fill the tank while Tap3 takes half the time taken by Tap2 and Tap4 takes half the time taken by Tap3. Similarly each next number of tap takes half the time taken by previous number of Tap i.e, K-th Tap takes half the time taken by (K-1)th Tap.If the 10th tap takes 2 hours to fill the tank alone then what is the ratio of efficiency of 8th tap and 12th tap, respectively?

Pipes A, B and C are attached to an empty cistern. While the first two can fill the cistern in 4 and 10 hrs, respectively, the third can drain the cistern, when filled, in 6 hrs. If all the three pipes are opened simultaneously when the cistern is half-full, how many hours will be needed to fill the cistern?

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