Two water taps together can fill a tank in 75/8 hours. The tap of the longer…
2024
Two water taps together can fill a tank in 75/8 hours. The tap of the longer diameter takes 10 hours less than the smaller one to fill the tank separately. The time in which the smaller tap can fill the tank separately is :
- A.
25 hours
- B.
10 hours
- C.
15 hours
- D.
15/4 hours
Attempted by 8 students.
Show answer & explanation
Correct answer: A
Answer: 25 hours
Let the smaller tap take x hours; then the larger tap takes x - 10 hours.
Combined filling rate: 1/x + 1/(x - 10) = 8/75. Simplify to form a quadratic:
(2x - 10)/(x^2 - 10x) = 8/75, which leads to 75(2x - 10) = 8(x^2 - 10x) and then 8x^2 - 230x + 750 = 0.
Solve the quadratic: discriminant = 230^2 - 4·8·750 = 28900 = 170^2. So x = (230 ± 170)/16, giving x = 25 or x = 15/4.
Reject x = 15/4 because x must be greater than 10 (so that x - 10 > 0). Therefore x = 25 hours is the valid solution.
Check: smaller = 25 h, larger = 15 h. Combined rate = 1/25 + 1/15 = (3 + 5)/75 = 8/75, matching the given combined time.