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# [Smart Math] Percentages Problem 23

Here’s and example of a SMART MATH problem for PERCENTAGES.

### Problem

If the population increases by 3% per annum, what will be the population of the city 2 years hence, if it is 81250 now?

1. 86198
2. 87189
3. 85988
4. 88198
5. 85189

### The Usual Method

Population 2 years hence will be:

$81250\times \left( 1+\frac{3}{100} \right)^{2}$

= 81250 x 1.0609

= 86198

(Ans: 1)

Estimated Time to arrive at the answer = 45 seconds.

### Using Technique

Population 2 years hence can be approximated using 81250 as 80000 and instead of 3% cumulative over 2 years take 3% additive over 2 years i.e. 6% of 80000 = 4800 (+)

Hence approximate population = 81250 + 4800(+) = 86050(+)

(Note: The (+) sign denotes that the actual answer will be slightly greater than 86050 since our assumption of taking 3% addition as 6% will yield a value lesser than 3% cumulative.

Also 80000 (Approximated) < 81250 (Actual).

Hence actual increase will be slightly greater than 4800. Hence the (+) sign)

As can be seen from the options, only option ‘1’ is closest to 86050 and slightly greater than that.

(Ans: 1)

Estimated Time to arrive at the answer = 15 seconds.
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