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Three taps A, B & C can fill the swimming pool with uniform flow. If taps A & B are left open simultaneously, it can fill the swimming pool in the same time in which tap C alone can fill the swimming pool. However, tap B fills the pool 10 hours faster as compared to tap A and 8 hours slower as compared to tap C. In how much time tap A can fill the entire pool?

Three taps A, B & C can fill the swimming pool with uniform flow. If taps A & B are left open simultaneously, it can fill the swimming pool in the same time in which tap C alone can fill the swimming pool. However, tap B fills the pool 10 hours faster as compared to tap A and 8 hours slower as compared to tap C. In how much time tap A can fill the entire pool? Correct Answer 30 hours

Suppose tap A requires ‘a’ hours to fill the entire swimming pool

⇒ Time taken by tap B and tap C = (a – 10) & (a – 18) respectively to fill the entire tank

⇒ ∴ 1/a + 1/(a – 10) = 1/(a – 18)

⇒ (a – 10 + a) / = 1/(a – 18)

⇒ (2a – 10) / = 1/(a – 18)

⇒ 2a2 – 36a – 10a + 180 = a2 – 10a

⇒ a2 – 36a + 180 = 0

⇒ a2 – 30a – 6a + 180 = 0

⇒ a(a – 6) – 30(a – 6) = 0

⇒ a = 6 or 30;

If a = 6 then Tap B fills tank in 6 – 10 = -4 hrs (absurd)

So, a = 30; Tap B fills tank in 30 – 10 = 20hrs and Tap C fills in 30 – 18 = 12 hrs

∴ tap A fills tank in 30 hrs

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