Observe the populations of some Indian cities in the table below. Rank City Population (2011) Population (2001) 1 Mumbai 1,24,42,373 1,19,78,450 2 New Delhi 1,10,07,835 98,79,172 3 Bengaluru 84,25,970 43,01,326 4 Hyderabad 68,09,970 36,37,483 5 Ahmedabad 55,70,585 35,20,085 6 Chennai 46,81,087 43,43

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.

Rank City Population (2011) Population (2001) 1 Mumbai 1,24,42,373 1,19,78,450 2 New Delhi 1,10,07,835 98,79,172 3 Bengaluru 84,25,970 43,01,326 4 Hyderabad 68,09,970 36,37,483 5 Ahmedabad 55,70,585 35,20,085 6 Chennai 46,81,087 43,43,645 7 Kolkata 44,86,679 45,72,876 8 Surat 44,67,797 24,33,835 9 V

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 .

NCERT Solutions for Class 7th Maths Chapter 1 .4 Exact and Approximate Values — Populations of Cities

Book page 131 Updated on2026-09-19

Q1.

Observe the populations of some Indian cities in the table below.

Rank	City	Population (2011)	Population (2001)
1	Mumbai	1,24,42,373	1,19,78,450
2	New Delhi	1,10,07,835	98,79,172
3	Bengaluru	84,25,970	43,01,326
4	Hyderabad	68,09,970	36,37,483
5	Ahmedabad	55,70,585	35,20,085
6	Chennai	46,81,087	43,43,645
7	Kolkata	44,86,679	45,72,876
8	Surat	44,67,797	24,33,835
9	Vadodara	35,52,371	16,90,000
10	Pune	31,15,431	25,38,473
11	Jaipur	30,46,163	23,22,575
12	Lucknow	28,15,601	21,85,927
13	Kanpur	27,67,031	25,51,337
14	Nagpur	24,05,665	20,52,066
15	Indore	19,60,631	14,74,968
16	Thane	18,18,872	12,62,551
17	Bhopal	17,98,218	14,37,354
18	Visakhapatnam	17,28,128	13,45,938
19	Pimpri-Chinchwad	17,27,692	10,12,472
20	Patna	16,84,222	13,66,444

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.

Rank	City	Population (2011)	Population (2001)
1	Mumbai	1,24,42,373	1,19,78,450
2	New Delhi	1,10,07,835	98,79,172
3	Bengaluru	84,25,970	43,01,326
4	Hyderabad	68,09,970	36,37,483
5	Ahmedabad	55,70,585	35,20,085
6	Chennai	46,81,087	43,43,645
7	Kolkata	44,86,679	45,72,876
8	Surat	44,67,797	24,33,835
9	Vadodara	35,52,371	16,90,000
10	Pune	31,15,431	25,38,473
11	Jaipur	30,46,163	23,22,575
12	Lucknow	28,15,601	21,85,927
13	Kanpur	27,67,031	25,51,337
14	Nagpur	24,05,665	20,52,066
15	Indore	19,60,631	14,74,968
16	Thane	18,18,872	12,62,551
17	Bhopal	17,98,218	14,37,354
18	Visakhapatnam	17,28,128	13,45,938
19	Pimpri-Chinchwad	17,27,692	10,12,472
20	Patna	16,84,222	13,66,444

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.

City	2011	2001	Increase
Bengaluru	84,25,970	43,01,326	41,24,644
Hyderabad	68,09,970	36,37,483	31,72,487
Ahmedabad	55,70,585	35,20,085	20,50,500
Surat	44,67,797	24,33,835	20,33,962
Vadodara	35,52,371	16,90,000	18,62,371
Mumbai	1,24,42,373	1,19,78,450	4,63,923

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.

City	2001	2011	Roughly how many times
Vadodara	16,90,000	35,52,371	about 2.1 times
Bengaluru	43,01,326	84,25,970	about 2 times
Hyderabad	36,37,483	68,09,970	about 1.9 times
Surat	24,33,835	44,67,797	about 1.8 times
Pimpri-Chinchwad	10,12,472	17,27,692	about 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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