Case Study III Two water taps together fill a tank in 1 hours. The tap with larger diameter takes 2 hours less than the tap with smaller one to fill the tank completely. Based on the above information, answer the following questions: 1\. If time taken by the tap with smaller diameter to fill the tank alone be x hours, then part of the tank filled by the tap with larger diameter alone in 2 hours is: 1. 2(x + 2) 2. 2(x - 2) 3. 2/(x + 2) 4. 2/(x − 2) 2\. The quadratic equation representing the given information is: 1. 4x² − 23x + 15 = 0 2. 2x² − 23x + 15 = 0 3. 4x² + 23x − 15 = 0 4. 2x² + 23x − 15 = 0 3\. Time taken by the larger tap to fill the tank alone is: 1. 5 hours 2. 3 hours 3. 7 hours 4. none of these 4\. The part of the tank which can be filled by the smaller tap in 3 hours is: 1. 1/3 2. 1/5 3. 3/5 4. 3/7 5\. The part of the tank which can be filled by the larger tap in hours is: 1. 5/12 2. 3/5 3. 5/8 4. 3/8

Question

Case Study III Two water taps together fill a tank in 1 hours. The tap with larger diameter takes 2 hours less than the tap with smaller one to fill the tank completely. Based on the above information, answer the following questions: 1\. If time taken by the tap with smaller diameter to fill the tank alone be x hours, then part of the tank filled by the tap with larger diameter alone in 2 hours is: 1. 2(x + 2) 2. 2(x - 2) 3. 2/(x + 2) 4. 2/(x − 2) 2\. The quadratic equation representing the given information is: 1. 4x² − 23x + 15 = 0 2. 2x² − 23x + 15 = 0 3. 4x² + 23x − 15 = 0 4. 2x² + 23x − 15 = 0 3\. Time taken by the larger tap to fill the tank alone is: 1. 5 hours 2. 3 hours 3. 7 hours 4. none of these 4\. The part of the tank which can be filled by the smaller tap in 3 hours is: 1. 1/3 2. 1/5 3. 3/5 4. 3/7  5\. The part of the tank which can be filled by the larger tap in hours is: 1. 5/12 2. 3/5 3. 5/8 4. 3/8

KnowledgeBoat · Accepted Answer

1\. Let time taken by smaller tap to fill tank = x hours Part of tank filled by smaller tap in one hour = Time taken by larger tap to fill tank = (x - 2) hours Part of tank filled by larger tap in one hour Part of tank filled by larger tap in two hour Hence, option (4) is the correct option. 2\. Given, Together smaller and larger tap take hours to fill tank. Rate at which the taps fill tank in one hour = tank/hr From question 1 we have, Part of tank filled by smaller tap in one hour = Part of tank filled by larger tap in one hour = Hence, option (1) is the correct option. 3\. Solving equation from question 2, ⇒ 4x2 - 23x + 15 = 0 ⇒ 4x2 - 20x - 3x + 15 = 0 ⇒ 4x(x - 5) - 3(x - 5) = 0 ⇒ (4x - 3)(x - 5) = 0 ⇒ (4x - 3) = 0 or (x - 5) = 0 [Using zero-product rule] ⇒ x = or x = 5 Case 1 : x = Larger tap take (x - 2) hours = = -1.25 hours, which is not possible. Case 2 : x = 5 The time taken by the smaller tap is x = 5 hours. The time taken by the larger tap is x − 2 = 5 - 2 = 3 hours. Hence, option (2) is the correct option. 4\. The smaller tap fills the tank in x = 5 hours. Part of tank filled by smaller tap in one hour = Part of tank filled by smaller tap in 3 hours = Hence, option (3) is the correct option. 5\. The larger tap fills the tank in 3 hours. Part of tank filled by larger tap in one hour Part of tank filled by larger tap in hours = = Hence, option (1) is the correct option.

Mathematics

Quadratic Equations

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