Let the smaller diameter tap fill the reservoir in ‘a’ hours
Larger diameter tap fills it in ‘a – 10’ hours.
Given, two water taps together can fill a tank in \(9\frac{3}{8}=\) 75/8 hours.
In 1 hour, part of tank filled = 8/75
\(\Rightarrow \frac{1}{a}+\frac{1}{a\,-\,10}=\frac{8}{75}\)
⇒ 75(a + a – 10) = 8a2 – 80a
⇒ 150a – 750 = 8a2 – 80a
⇒ 8a2 – 230a + 750 = 0
⇒ 4a2 – 115a + 375 = 0
⇒ 4a2 – 100a – 15a + 375 = 0
⇒ 4a(a – 25) – 15(a – 25) = 0
⇒ (4a – 15)(a – 25) = 0
Value of a can’t be 15/4 as (a – 10) will be negative
Thus a = 25
Time taken by faster tap = 25 – 10 = 15 hours