Question

Two villages Ramnagar and Jamnagar had same population 2 years ago. Population of
Ramnagar decreased at R% p.a. while population of Jamnagar increased at R% p.a.
Today, the difference between their population is 1000R, then what was the

population of any village 2 years ago?​

Answer 1

Hope this helps you !!!

Answer 2

Solution :-

Let us assume that, both villages has population x 2 years ago.

now,

• Population of Ramnagar decreased at R% p.a.
• Population of Jamnagar increased at R% p.a.

then,

→ Present Population of Ramnagar = initial Population * [1 - (% dec./100)]² = x[ 1 - (R/100)]²

and,

→ Present Population of Ramnagar = initial Population * [1 + (% inc./100)]² = x[ 1 + (R/100)]²

given that, the difference between their population is 1000R .

therefore,

→ x[ 1 + (R/100)]² - x[ 1 - (R/100)]² = 1000R

→ x[{1 + (R/100)}² - {1 - (R/100)}²] = 1000R

→ x[{(100 + R)²/10000} - {(100 - R)²/10000}] = 1000R

→ x[(10000 + R² + 200R) - (10000 + R² - 200R)] / 10000 = 1000R

→ x[10000 - 10000 + R² - R² + 200R + 200R] = 1000R * 10000

→ x * 400R = 1000R * 10000

→ 4x = 10 * 10000

→ x = 25,000 (Ans.)

Hence , the Population of both villages was 25,000 before 2 years.

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