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Present population of city A and B are 73,205 and 32,805, respectively. Increasing and decreasing rate of population in the city are same (Increasing in city A and decreasing in city B), and is 10%. Find how many years ago, population of both city were same.

Present population of city A and B are 73,205 and 32,805, respectively. Increasing and decreasing rate of population in the city are same (Increasing in city A and decreasing in city B), and is 10%. Find how many years ago, population of both city were same. Correct Answer 4 years

Given:

Present population of city A = 73,205

Present population of city B = 32,805

Decreasing and increasing rate is same as 10%

Concept used:

Population n year ago if present population is P = , where + /- sign indicate the increasing /decreasing rate.

Calculation:

Let after n years, population are same.

In A, Population n year ago = 73205/ (1 + 10/100) n     ----(i)

Using formula, population n year ago if present population is P = , where + /- sign indicate the increasing /decreasing rate.

In B, Population n year ago = 32805 / (1 – 10/100) n     ---- (2)

After equating equation (1) and (2)

⇒ 73205/ (1 + 10/100) n = 32805 / (1 – 10/100) n

⇒ 14641/ (1 + 10/100) n = 6561/ (1 – 10/100) n

⇒ (121)2/(11)n = (81)2/(9)n

⇒ 114/11n = 94/9n

⇒ n = 4

∴ The population was same 4 years ago

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