Important Quadratic Equations related Questions.
Diameter based quadratic equations questions are a type of mathematical problem that involve using the concept of diameter, flow rate and time to fill a tank.
NCERT Solutions for Class 10th Maths.
EXERCISE 4.3 Questions No:9
Two water taps together can fill a tank in 9(3/8) hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
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Let, the time taken by large tap to fill the tank = x hours
So, the time taken by smaller tap to fill the tank = x + 10 hours
Therefore, in 1 hour,
tank filled by larger tap = 1/x+10
According to question,
1/x + 1/x + 10 = 1/(9 (3/8))
⇒ x + 10 + x/x(x + 10) = 8/75
⇒ 75(2x + 10) = 8x(x + 10)
⇒ 150x +750 = 8x² + 80x
⇒ 8x² – 70x – 750 = 0
⇒ 4x² – 35x – 375 = 0
⇒ 4x² – 60x + 25x – 375 = 0
⇒ 4x(x – 15) + 25 (x – 15) = 0
⇒ (x – 15) (x + 25) = 0
⇒ (x – 15) = 0 or (x + 25) = 0
Either x = 15 or x = – 25
But, x ≠ – 25, as x is the time taken to fill the tank which can’t be negative. So, x
Hence, the time taken by larger top to fill the tank = 15 hours
and the time by smaller tap to fill the tank = 15 + 10 = 25 hours.