A reservoir has two pipes, A and B. A can fill the reservoir 5 hours faster than B. If both together fill the reservoir in 6 hours, the reservoir will be filled by A alone in-
বিকল্পসমূহ (নিজের উত্তর যাচাই করতে ক্লিক করুন):
সঠিক উত্তর
1 (10 hours)
বিস্তারিত ব্যাখ্যা ও বিশ্লেষণ:
Let:
- A alone can fill the reservoir in x hours
- B alone can fill it in x + 5 hours
Work done by A and B together in 1 hour =
(1/x) + (1/(x + 5)) = (2x + 5)/(x² + 5x)
Given: Both together can fill in 6 hours, so:
1 / [(2x + 5)/(x² + 5x)] = 1/6
⇒ (x² + 5x)/(2x + 5) = 6
⇒ x² + 5x = 12x + 30
⇒ x² - 7x - 30 = 0
x² - 10x + 3x - 30 = 0
x(x - 10) + 3(x - 10) = 0
(x - 10)(x + 3) = 0
Therefore:
- x = 10 or x = -3
- Since time can't be negative, x = 10
∴ A alone can fill the reservoir in: 10 hours
