In the first year the population of a town decreased by 5% due to the Corona virus first wave. In the next year it decreased again by 5% due to the second wave and in the third year it increased by 5%. At the end of the third year the population was 9,47,625. What was the population at the beginning of the first year?

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 08 Dec 2022 Shift 3)

Answer 1

Given:

Population at the end of the third year = 9,47,625

Let the initial population of the village is 'x'

Concept used :

5% of x =\(5x\over100\)

Calculations:

Initially, population is decreased by 5%.

5% of x =\(5x\over100\)

Now the population after decrement is:

\(x-{5x\over100}={95x\over100}\)

Population is further decreased by 5%:

5% of \({95x\over100}={95x\over100}×{5\over100}={475x\over10000}\)

Now the population after decrement is:

\({95x\over100}-{475x\over10000}={9025x\over10000}\)

Now the population is increased by 5%

5% of \({9025x\over10000}={9025x\over10000}×{5\over100}={45125x\over1000000}\)

Now the population after the increment is:

\({9025x\over10000}+{45125x\over1000000}={947625x\over1000000}\)

From the given initial conditions:

\({947625x\over1000000}\) = 947625

x = 1000000

Thus, the population at the beginning of the first year was 10,00,000.

Shortcut Trick

According to the question, 7581 unit → 947625

Then, 8000 unit → 947625/7581 × 8000 = 125 × 8000 = 1000000