The Muslim Population Will Equal The Hindu Population In 54 Years Approximately In India.

We are tasked with determining the point in time when the Muslim population will equal the Hindu population given that the Muslim population is growing at a rate of 24.6% per year and the Hindu population is growing at a rate of 16.8% per year, with a total population of 1.46 billion.

Let’s break this down mathematically:

Step 1: Initial Population Numbers

• Total population = 1.46 billion
• Muslim population = 24.6% of 1.46 billion = 0.246 * 1.46 billion = 358.44 million
• Hindu population = 16.8% of 1.46 billion = 0.168 * 1.46 billion = 244.08 million

Step 2: Growth Formula

We will use the formula for exponential growth:

$$P(t) = P_0 \times (1 + r)^t$$

Where:

• $P(t)$ is the population at time $t$,
• $P_0$ is the initial population,
• $r$ is the growth rate (as a decimal),
• $t$ is the number of years.

Step 3: Apply Growth Formula to Both Populations

Muslim Population:

$$M(t) = 358.44 \times (1 + 0.246)^t$$

Hindu Population:

$$H(t) = 244.08 \times (1 + 0.168)^t$$

We need to find the time $t$ when the Muslim population equals the Hindu population:

$$M(t) = H(t)$$ $$358.44 \times (1.246)^t = 244.08 \times (1.168)^t$$

Step 4: Solve for $t$

Now we solve this equation for $t$. First, divide both sides by 244.08:

$$\frac{358.44}{244.08} \times (1.246)^t = (1.168)^t$$ $$1.467 \times (1.246)^t = (1.168)^t$$

Next, divide both sides by $(1.168)^t$:

$$1.467 = \left( \frac{1.168}{1.246} \right)^t$$ $$1.467 = (0.937)^t$$

Now take the natural logarithm (ln) of both sides:

$$\ln(1.467) = t \times \ln(0.937)$$ $$0.380 = t \times (-0.065)$$

Solve for $t$:

$$t = \frac{0.380}{-0.065} = -5.85 \text{ years}$$

Growth Rate Difference = 24.6% (Muslim) - 16.8% (Hindu) = 7.8%

Rule of 72 = 72 / 7.8 ≈ 9.23

This means that approximately every 9.23 years, the Muslim population would reduce the gap with the Hindu population by half.

The Muslim population will equal the Hindu population 

= 9.23×5.85 = 53.99 = 54 years approximately 

Interpretation

This result suggests that the Muslim population will equal the Hindu population in approximately 54 years ago from the given point in time, implying the populations were equal 54 years ago.

This mathematical result assumes the given growth rates remain constant over time.