Question

5% of population of town were killed in an earthquake and 8% of the remainder left the town. If the population of the town now is 43700 , what was it population at the beginning?

Answer 1

Let the initial Population of the town be x

Then Population of the town after the earthquake = x - 5% of x
                                                                                              = 19x/20

Population of town after the 8% left the town = 19x/20 - 8% of 19x/20
                                                                                    = 437x/500

This population is equal to 43700

=>   437x/500=43700
=>   x= 50000


So, Population of the town at the beginning was 50000

Answer 2

A very good formula is used here to find the population at the beginning.
$\bold{P=\frac{P_1\times100\times\100}{(100-A)(100-B)}}$
Here, P is the population at the beginning .
P₁ is the population of town in present time.
A is the % of population of town were killed in an earthquake
B is the % of reminder left the town.

Given,
P₁ = 43700 , A = 5 % and B = 8 %
∴ P = 43700 × 100 × 100/(100 - 5) × (100 - 8)
= 43700 × 10000/(85 × 92)
= 4370 × 10⁵/8740
= 10⁵/2
= 50,000

Hence, population of town at the beginning is 50,000