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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 52

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

Ratio Proportion

Problem

A tank normally filled in 8 hours takes 2 hours longer owing to a leak. If the tank is full the leak shall empty in _________ hours?

  1. 16
  2. 20
  3. 25
  4. 40
  5. 45

The Usual Method

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It takes 8 hours for the tank to be filled, so \frac{1}{8} of the tank will be filled in 1 hour.

Owing to the leak, the tank is filled in 8 + 2 = 10 hours, so \frac{1}{10} of the tank will be filled in 1 hour.

Let the leak empty the tank in ‘x’ hours, so \frac{1}{x} of the tank will be emptied in 1 hour.

\therefore \frac{1}{8}-\frac{1}{x}=\frac{1}{10}

\therefore \frac{1}{x}=\frac{1}{8}-\frac{1}{10}

\therefore \frac{1}{x}=\frac{2}{80}=\frac{1}{40}

\therefore x=40hours.

(Ans: 4)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

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Since \frac{1}{8} tank is filled in 1 hour by the inlet working alone and \frac{1}{10} of the tank is filled in 1 hour by keeping both the inlet and the leak open, the time needed for the outlet to empty the tank should be both a multiple of 8 and 10. (Note: \frac{1}{8}-\frac{1}{x}=\frac{1}{10} and \frac{1}{x}=\frac{1}{8}-\frac{1}{10}) The only option satisfying this criteria is option ‘4’.

(Ans: 4)

Estimated Time to arrive at the answer = 10 seconds.
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