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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 36

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

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

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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.

Using Technique

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Instead of assuming that 2 taps are kept open for 2 minutes each, assume that one tap is kept open for 4 minutes. Thus if a tap takes 18 minutes to fill and kept open for 4 minutes, balance time that it has to be kept open for further filling up the tank = 18 – 4 = 14 minutes. Now the answer has to be in the proximity of 14 minutes but less than 14 since the 1st tap fills the tank in 12 minutes only which is lesser than the time it takes to only fill it up by the 2nd tap. Hence, 13 minutes.

(Ans: 5)

Estimated Time to arrive at the answer = 10 seconds.
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