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

**Problem**

**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?

- 86198
- 87189
- 85988
- 88198
- 85189

**The Usual Method**

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Population 2 years hence will be:

= 81250 x 1.0609

= 86198

**(Ans: 1)**

*Estimated Time to arrive at the answer = 45 seconds.*

**Using Technique**

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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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