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[Smart Math] Ratio Proportion Problem 52

Here’s and example of a SMART MATH problem for 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

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.

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

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

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

$\therefore x=40$hours.

(Ans: 4)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

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’.