Multiple choice

If two pipes operates simultaneously, a tank is filled in 12 hours. One pipe fills the tank in 10 hours faster than the other. In how many hours does the faster pipe alone take to fill the tank? यदि दो नलियाँ एक साथ चालू हों, तो एक टंकी 12 घंटों में भर जाती है। उनमें एक नली उस टंकी को दूसरी की अपेक्षा 10 घंटे अधिक की गति से भर देती है। तदनुसार, वह तेज गति वाली नली अकेली, उस टंकी को कितने घंटों में भर देगी?

  1. 20

  2. 18

  3. 15

  4. 12
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A Correct answer
Explanation

Let slower pipe take x hours, so faster takes (x-10) hours. Together: 1/x + 1/(x-10) = 1/12. Solving: (2x-10)/[x(x-10)] = 1/12, giving x² - 10x = 24x - 120, so x² - 34x + 120 = 0. This gives x = 30 (valid) or x = 4 (invalid as x-10 would be negative). Faster pipe takes 30-10 = 20 hours.

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