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Two water pipes together can fill a tank in9/3/8 the pipe of larger diameter takes 10 hours less than the smaller one to fill the tank separately find the time in which each pipe can fill the tank separately |
| Answer» <html><body><p><strong>Answer:</strong></p><p>Answer:</p><p></p><p>Let the tap with <a href="https://interviewquestions.tuteehub.com/tag/smaller-1213327" style="font-weight:bold;" target="_blank" title="Click to know more about SMALLER">SMALLER</a> diameter fills the tank alone in <a href="https://interviewquestions.tuteehub.com/tag/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a> <a href="https://interviewquestions.tuteehub.com/tag/hours-1030090" style="font-weight:bold;" target="_blank" title="Click to know more about HOURS">HOURS</a></p><p></p><p>Let the tap with larger diameter fills the tank alone in (x – 10) hours.</p><p></p><p>In 1 hour, the tap with a smaller diameter can <a href="https://interviewquestions.tuteehub.com/tag/fill-987981" style="font-weight:bold;" target="_blank" title="Click to know more about FILL">FILL</a> 1/x part of the tank.</p><p></p><p>In 1 hour, the tap with larger diameter can fill 1/(x – 10) part of the tank.</p><p></p><p>The tank is filled up in 75/8 hours.</p><p></p><p>Thus, in 1 hour the taps fill 8/75 part of the tank.</p><p></p><p>1/x + 1/(x-10) = 8/75</p><p></p><p>(x-10) + x / x(x-10) = 8/75</p><p></p><p>2x – 10/x(x-10) = 8/75</p><p></p><p>75 (2x-10) = 8(x2-10x) by cross multiplication</p><p></p><p>150x – 750 = 8x2 – 80x</p><p></p><p>8x2 − 230x + 750 = 0</p><p></p><p>4x2−115x + 375 = 0</p><p></p><p>4x2 − 100x −15x + 375 = 0</p><p></p><p>4x(x−25)−15(x−25) = 0</p><p></p><p>(4x−15)(x−25) = 0</p><p></p><p>4x−15 = 0 or x – 25 = 0</p><p></p><p>x = 15/4 or x = 25</p><p></p><p>Case 1: When x = 15/4</p><p></p><p>Then x – 10 = 15/4 – 10</p><p></p><p>⇒ 15-40/4</p><p></p><p>⇒ -25/4</p><p></p><p>Time can never be negative, so x = 15/4 is not possible.</p><p></p><p>Case 2: When x = 25 then</p><p></p><p>x – 10 = 25 – 10 = 15</p><p></p><p>∴ The tap of smaller diameter can separately fill the tank in 25 hours, and the time taken by the larger tap to fill the tank = (25 – 10) = 15 hours.</p><p><strong></strong></p><p></p></body></html> | |