Two water taps together can fill a tank in
2×11/12 hrs. The tap of smaller diameter takes 2
hours more than the larger one to fill the tank
separately. Find the time in which each tap can
separately fill the tank.
Answers
Answer:
ANS:- 5
Step-by-step explanation:
Let the tap of larger diameter takes time to fill the tank = x hrs
Then, the tap of smaller diameter takes time to fill the tank = (x + 2) hrs
In 1 hour, tap of larger diameter will fill = 1/x part of tank
In 1 hour, tap of smaller diameter will = (1/x + 2) part of tank
Together, both the taps take time to fill the tank = 2 11/12 hrs
In 1 hour, both the taps will fill = 12/35 part of tank
∴ 1/x + 1/(x + 2) = 12/35
Taking the LCM and then solving it.
⇒ (x + 2 + 2)/(x + 2)(x) = 12/35
⇒ (2x + 2)/(x² + 2x) = 12/35
⇒ 12x² + 24x = 70x + 70
⇒ 12x² + 24x - 70x - 70 = 0
⇒ (12x² - 46x - 70 = 0) ÷ 2
⇒ 6x² - 23x - 35 = 0
⇒ 6x² - 30x + 7x - 35 = 0
⇒ 6x(x - 5) + 7(x - 5) = 0
⇒ (6x + 7) = 0 or (x - 5) = 0
⇒ x = - 7/6 or x = 5
x = - 6/7 is not possible because time cannot be negative. So, the correct value of x is 5.
So, time taken by tap of larger diameter is 5 hours and time taken by tap of smaller diameter is 5 + 2 = 7 hours separately.
Solution :-
Let the tap of larger diameter takes time to fill the tank = x hrs
Then, the tap of smaller diameter takes time to fill the tank = (x + 2) hrs
In 1 hour, tap of larger diameter will fill = 1/x part of tank
In 1 hour, tap of smaller diameter will = (1/x + 2) part of tank
Together, both the taps take time to fill the tank = 2 11/12 hrs
In 1 hour, both the taps will fill = 12/35 part of tank
∴ 1/x + 1/(x + 2) = 12/35
Taking the LCM and then solving it.
⇒ (x + 2 + 2)/(x + 2)(x) = 12/35
⇒ (2x + 2)/(x² + 2x) = 12/35
⇒ 12x² + 24x = 70x + 70
⇒ 12x² + 24x - 70x - 70 = 0
⇒ (12x² - 46x - 70 = 0) ÷ 2
⇒ 6x² - 23x - 35 = 0
⇒ 6x² - 30x + 7x - 35 = 0
⇒ 6x(x - 5) + 7(x - 5) = 0
⇒ (6x + 7) = 0 or (x - 5) = 0
⇒ x = - 7/6 or x = 5
x = - 6/7 is not possible because time cannot be negative. So, the correct value of x is 5.
So, time taken by tap of larger diameter is 5 hours and time taken by tap of smaller diameter is 5 + 2 = 7 hours separately.
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