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NCERT Solutions Ganita Prakash (Part 1) Chapter 1 .4 Exact and Approximate Values — Populations of Cities

Book page 131 Updated on2026-09-05

Q1.
From the information given in the table, answer the following questions by approximation: What is your general observation about this data? Share it with the class.
Answer

Almost every city in the table grew between 2001 and 2011 — several of them enormously — and only one shrank.

  • The top two, Mumbai and New Delhi, are the only cities above 1 crore (1,24,42,373 and 1,10,07,835 in 2011).
  • Bengaluru, Hyderabad, Surat and Vadodara nearly doubled in ten years.
  • Kolkata is the only city that lost people — it fell from 45,72,876 to 44,86,679, a drop of about 86,000.
  • Mumbai grew by only about 4.6 lakh, far less than Bengaluru's 41 lakh, so being the biggest does not mean growing the fastest.
  • All 20 cities in the table had more than 16 lakh people in 2011.
Why it happens: Cities with fast-growing industries and IT work (Bengaluru, Hyderabad, Surat, Pune, Pimpri-Chinchwad) pulled in people from other places, while already-crowded old cities such as Kolkata and Mumbai grew slowly or not at all.
Q2.
What is an appropriate title for the above table?
Answer

A good title names the what, the where and the when. For example:

  • “Population of the 20 largest Indian cities, 2001 and 2011”
  • “Census populations of major Indian cities (2001 vs 2011)”
  • “Twenty most populous Indian cities and how they grew, 2001–2011”
Why it happens: The table has three pieces of information in it — a rank, a city name, and two population columns dated 2001 and 2011. A title that leaves out the years would not tell a reader that the table is about change over time.
Q3.
How much is the population of Pune in 2011? Approximately, by how much has it increased compared to 2001?
Answer

Pune's 2011 population is 31,15,431, an increase of about 6 lakh over 2001.

Population in 2011 = 31,15,431
Population in 2001 = 25,38,473
Increase = 31,15,431 − 25,38,473 = 5,76,958
Rounded to the nearest lakh = about 6,00,000 (6 lakh)
Why it happens: Round first and the mental arithmetic is easy: about 31 lakh minus about 25 lakh is about 6 lakh. The exact subtraction confirms it — 5,76,958 rounds to 6 lakh.
Q4.
Which city’s population increased the most between 2001 and 2011?
Answer

Bengaluru, by 41,24,644 people — more than 41 lakh.

City20112001Increase
Bengaluru84,25,97043,01,32641,24,644
Hyderabad68,09,97036,37,48331,72,487
Ahmedabad55,70,58535,20,08520,50,500
Surat44,67,79724,33,83520,33,962
Vadodara35,52,37116,90,00018,62,371
Mumbai1,24,42,3731,19,78,4504,63,923
Why it happens: Bengaluru added more people in ten years than the entire 2011 population of Pune. Notice that Mumbai, though far larger, added less than 5 lakh — a big population and a big increase are two different things.
Q5.
Are there cities whose population has almost doubled? Which are they?
Answer

Yes — Bengaluru, Hyderabad, Surat and Vadodara. Vadodara has more than doubled.

City20012011Roughly how many times
Vadodara16,90,00035,52,371about 2.1 times
Bengaluru43,01,32684,25,970about 2 times
Hyderabad36,37,48368,09,970about 1.9 times
Surat24,33,83544,67,797about 1.8 times
Pimpri-Chinchwad10,12,47217,27,692about 1.7 times
Why it happens: To check “doubled”, ask whether the 2001 figure doubled is still smaller than the 2011 figure. For Vadodara, 16,90,000 × 2 = 33,80,000, and 35,52,371 is bigger — so it has more than doubled. For Bengaluru, 43,01,326 × 2 = 86,02,652, just above 84,25,970 — so it is almost double.
Q6.
By what number should we multiply Patna’s population to get a number/population close to that of Mumbai?
Answer

By about 7 (more precisely about 7.4).

Patna (2011) = 16,84,222 ≈ 17 lakh
Mumbai (2011) = 1,24,42,373 ≈ 124 lakh
124 ÷ 17 ≈ 7.3

Check: 16,84,222 × 7 = 1,17,89,554 (a bit less than Mumbai)
16,84,222 × 8 = 1,34,73,776 (a bit more than Mumbai)
Why it happens: 7 times Patna falls about 6.5 lakh short and 8 times overshoots by about 10 lakh, so 7 is the closer whole number. Doing the division exactly gives 1,24,42,373 ÷ 16,84,222 ≈ 7.39.
Tip: For quick comparisons, round both numbers to lakhs first. 124 ÷ 17 is far easier to judge than 1,24,42,373 ÷ 16,84,222.
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