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**

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**

Note that the time taken if all the three are opened simultaneously cannot be 2 hours since there is something being withdrawn and something being added and that .

Similarly the time also cannot be 3 hours since there is something being withdrawn and something being added and that .

(Note: If the amount added and the amount withdrawn in a given time period are equal, the net effect is nil.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

[Smart Math] Ratio Proportion Problem 51,We hope this helps you in getting to the answer faster. You can apply this technique in the exams and get to the answer before anyone else can.

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