Question
Two taps A and B can fill a cistern in 12 min and 16 min
respectively. If both taps are opened together and at the end of 4 min, B tap is turned off, then how much time will it take to fill the cistern?Solution
Tap A fills the tank in 12 minutes → So, in 1 minute, it fills 1/12
Tap B fills the tank in 16 minutes → So, in 1 minute, it fills 1/16
Both taps are open for 4 minutes:
In 1 minute, together they fill: 1/12 + 1/16 = 7/48 ​
In 4 minutes, they fill: 7/48 × 4 = 28/48 =7/12 ​
B is turned off. Only A fills the rest.
Remaining to fill: 1−7/12 = 5/12
A fills 1/12 per minute, so time to fill 5/12: 5/12 ÷ 1/12 = 5 minutes
I. 3x2 = 2x2 + 9x – 20
II. 3y2 = 75
Equation 1: x² - 45x + 500 = 0
Equation 2: y² - 60y + 600 = 0
I. x2 + 24x + 143 = 0
II. y2 + 12y + 35 = 0
- If the quadratic equation x² + 18x + n = 0 has real and equal roots, what is the value of n?
I. 3p² - 14p + 15 = 0
II. 15q² - 34q + 15 = 0
I. x=  √(20+ √(20+ √(20+ √(20…………….∞)) ) )Â
II. y= √(5√(5√(5√(5……….∞)) ) )Â
...I. 10p² + 21p + 8 = 0
II. 5q² + 19q + 18 = 0
I. 117x² + 250x + 117 = 0
II. 54y² -123y + 65 = 0
Solve the quadratic equations and determine the relation between x and y:
Equation 1: x² - 36x + 288 = 0
Equation 2: y² - 36y + 320 = 0
I. 8/(21x) - 2/7 = 0
II. 16y² - 24y +9 = 0
