Question

Village P has a population of 78000, which is decreasing at the rate of 1800 per year. Village Q has a population of 54000, which is increasing at the rate of 600 per year. In how many years will the population of the two villages be equal?

• A. 14
• B. 15
• C. 10
• D. 12

Hint:

The "relative rate of closure" is the sum of the rates since one is increasing and the other is decreasing. Time = \(\frac{\text{Initial Difference}}{\text{Sum of Rates}} = \frac{24000}{2400} = 10\).

Answer 1

The Correct Option is C

Concept: This is a relative rate problem. Let \(n\) be the number of years. \[ \text{Pop}_P - 1800n = \text{Pop}_Q + 600n \]
Step 1: Set up the equation.
\(78000 - 1800n = 54000 + 600n\)

Step 2: Solve for \(n\).
\(78000 - 54000 = 600n + 1800n\)
\(24000 = 2400n\)
\(n = 10\).