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# [Smart Math] Ratio Proportion Problem 51

Here’s and example of a SMART MATH problem for RATIO PROPORTION.

### Problem

A tap can fill a tank in 3 hours and another tap in 2 hours. An outlet can drain the tank completely in 4 hours. If all three are kept open, how long would it take to fill the tank completely?

1. 2 hours
2. 3 hours
3. 4 hours
4. The tank will never be full.
5. None of these.

### The Usual Method

If only the first tap is kept open, time taken to fill the tank completely = 3 hours.

Hence per hour, $\frac{1}{3}$ of the tank is full.

Similarly for the other tap takes 2 hours to fill the tank, so $\frac{1}{2}$ of the tank will be filled in one hour.

For the outlet, it takes 4 hours to empty the tank, so, $\frac{1}{4}$ of the tank will be empty in one hour.

If al three are open simultaneously than in one hour, $\frac{1}{3}$ + $\frac{1}{2}$$\frac{1}{4}$ = $\frac{7}{12}$ of the tank will be full in one hour. Hence for the tank to be completely full, it will take $\frac{12}{7}=1\frac{5}{7}$hours.

Hence answer is none of these.

(Ans: 5)

Estimated Time to arrive at the answer = 45 seconds.

### Using Technique

Note that the time taken if all the three are opened simultaneously cannot be 2 hours since there is something being withdrawn $\left( \frac{1}{4} \right)$ and something being added $\left( \frac{1}{2} \right)$ and that $\frac{1}{4}\ne \frac{1}{2}$.

Similarly the time also cannot be 3 hours since there is something being withdrawn $\left( \frac{1}{4} \right)$ and something being added $\left( \frac{1}{3} \right)$ and that $\frac{1}{4}\ne \frac{1}{3}$.

(Note: If the amount added and the amount withdrawn in a given time period are equal, the net effect is nil. But in this particular problem, it is not the case).

Similarly the time cannot be 4 hours since the two pipes fill the tank in a time much less than 2 and 3 hours.

Also since $\frac{1}{2}+\frac{1}{3}>\frac{1}{4}$ the tank will get eventually filled. Thus all options being eliminated, only option ‘5’ is the answer.

(Ans: 5)

Estimated Time to arrive at the answer = 30 seconds.
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