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

**Problem**

**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?

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

**The Usual Method**

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

Hence per hour, of the tank is full.

Similarly for the other tap takes 2 hours to fill the tank, so of the tank will be filled in one hour.

For the outlet, it takes 4 hours to empty the tank, so, of the tank will be empty in one hour.

If al three are open simultaneously than in one hour, + – = of the tank will be full in one hour. Hence for the tank to be completely full, it will take hours.

Hence answer is none of these.

**(Ans: 5)**

*Estimated Time to arrive at the answer = 45 seconds.*

**Using Technique**

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Note that the time taken if all the three are opened simultaneously cannot be 2 hours since there is something being withdrawn and something being added and that .

Similarly the time also cannot be 3 hours since there is something being withdrawn and something being added and that .

(Note: If the amount added and the amount withdrawn in a given time period are equal, the net effect is nil.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 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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