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# [Smart Math] Ratio Proportion Problem 36

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

### Problem

Two taps can fill a tank in 12 and 18 minutes respectively. Both are kept open for two minutes and then the first is turned off. In how many minutes more will the tank be filled?

1. 9 minutes
2. 10 minutes
3. 11 minutes
4. 12 minutes
5. 13 minutes

### The Usual Method

The first tap will fill $\frac{1}{12}$th of the tank in 1 minute and

The second tap will fill $\frac{1}{18}$th of the tank in 1 minute.

Hence both working together will fill $\frac{1}{12}+\frac{1}{18}=\frac{5}{36}$ of the tank in 1 minute.

Hence in 2 minutes, $\frac{5}{36}\times 2=\frac{10}{36}$ of the tank will be full. Thus $\frac{26}{36}$ of the tank will be empty.

Now the 1st tap is closed, so the balance $\frac{26}{36}$ of the tank has to be filled by the 2nd tap. Thus 2nd tap takes 1 minute to fill $\frac{1}{18}$th of the tank, it will take 13 minutes to fill $\frac{26}{36}$ of the tank (using cross multiplication).

(Ans: 5)

Estimated Time to arrive at the answer = 45 seconds.