Question 13 Marks
A cistern has two taps attached to it. Tap B can empty the cistern in 45 minutes. But Tap A can fill the cistern in just 30 minutes. Rohit started both taps unknowingly but realized his mistake after 30 minutes. He immediately closed Tap B. Now, in how many minutes the cistern will be filled?
Answer
View full question & answer→In 1 minute, cistern filled by Tap $A=\frac{1}{30}$
In 1 minute, cistern emptied by Tap $B=\frac{1}{45}$
In 1 minute with Taps A and B, cistern filled $=\frac{1}{30}-\frac{1}{45}=\frac{1}{90}$
In 30 minutes, $30 \times \frac{1}{90}=\frac{1}{3}$ amount of cistern is filled
Remaining cistern $=1-\frac{1}{3}=\frac{2}{3}$
This is filled by Tap A only
In 1 minute, $\frac{1}{30}$ part of cistern is filled
In x minutes, $\frac{2}{3}$ amount of cistern is filled
$\therefore$ x minutes $=\frac{\frac{2}{3}}{\frac{1}{30}}$$= 20$ minutes
$20$ minutes $=$ Time to fill after Tap B is closed
In 1 minute, cistern emptied by Tap $B=\frac{1}{45}$
In 1 minute with Taps A and B, cistern filled $=\frac{1}{30}-\frac{1}{45}=\frac{1}{90}$
In 30 minutes, $30 \times \frac{1}{90}=\frac{1}{3}$ amount of cistern is filled
Remaining cistern $=1-\frac{1}{3}=\frac{2}{3}$
This is filled by Tap A only
In 1 minute, $\frac{1}{30}$ part of cistern is filled
In x minutes, $\frac{2}{3}$ amount of cistern is filled
$\therefore$ x minutes $=\frac{\frac{2}{3}}{\frac{1}{30}}$$= 20$ minutes
$20$ minutes $=$ Time to fill after Tap B is closed
