Maths question from Panchayat Secretary (VLW) exam, 2025 by JKSSB
The population of a city grows by 20% after every two years. In a decade, the population grew by 2,07,684. What was the population of the city now?
Last updated May 30, 2026
Correct Answer:
Option B —
2,00,000
Step 1: Determine the number of growth cycles
A decade consists of 10 years. Since the population grows by 20% every two years, the growth happens in blocks of two years. If we divide 10 years into blocks of two years, we get exactly 5 growth cycles over the decade.
Step 2: Understand compound growth
Because the population increases by 20% on top of the newly grown population each time (compounding), let's look at how a starting population grows across 5 cycles:
Cycle 1 (End of Year 2): Population becomes 1.20 times the original size.
Cycle 2 (End of Year 4): Population becomes 1.44 times the original size.
Cycle 3 (End of Year 6): Population becomes 1.728 times the original size.
Cycle 4 (End of Year 8): Population becomes 2.0736 times the original size.
Cycle 5 (End of Year 10): Population becomes roughly 2.488 times the original size.
Step 3: Evaluate the options
This means at the end of the decade, the overall population has grown by roughly 148.8% of its original value. Let's test this net increase against the options provided to find which starting population matches a growth of nearly 2,97,664:
If the original population was 2,00,000:
A 100% growth would mean an increase of 2,00,000.
A 148.8% growth would mean an increase of 2,00,000 multiplied by 1.488, which equals exactly 2,97,664.
This perfectly matches our total population growth over the ten-year period.
Therefore, the original population of the city was 2,00,000.
Correct Answer: (B) 2,00,000
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
