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NCERT Solutions Ganita Prakash (Part 2) Chapter 3 In-text Questions — Ratios in Maps

Book page 56 Updated on2026-09-05

Q1.
Have you noticed that in many maps there is a ratio given, usually in the lower right corner of the map? It usually contains 1 and a very large number, such as 1 : 60,00,000. What does RF 1 : 60,00,000 mean? What does it indicate? Can you guess?
Answer

It is the map’s scale: one unit of length on the paper stands for 60,00,000 of the same units on the ground.

1 cm on the map → 60,00,000 cm on the ground
1 mm on the map → 60,00,000 mm on the ground
1 inch on the map → 60,00,000 inches on the ground
Why it happens: An RF compares a length with a length, so the units cancel and the ratio has no unit at all. That is exactly why the same number works whichever ruler you pick up. It is called a Representative Fraction because it can also be written as the fraction 1/60,00,000.
  • A bigger second term (1 : 1,00,00,000) squeezes more ground onto the sheet, so the map shows a larger area in less detail.
  • A smaller second term (1 : 50,000) is a close-up — a city map — with much more detail.
  • The distance you get is the geographical (straight-line) distance, not the road distance. Roads bend, so a road is always longer.
Q2.
Convert 60,00,000 cm to kilometres. (It is 60 km. Verify this.)
Answer

Divide twice — once to reach metres, once to reach kilometres.

60,00,000 cm ÷ 100 = 60,000 m
60,000 m ÷ 1000 = 60 km
Why it happens: 1 m = 100 cm and 1 km = 1000 m, so 1 km = 1,00,000 cm. Then 60,00,000 ÷ 1,00,000 = 60 in one step. So the scale 1 : 60,00,000 can be read as the handy sentence “1 cm on the map = 60 km on the ground”.
Q3.
Using the map above, can you find the geographical distance between Bengaluru and Chennai? Also, find the geographical distance between Mangaluru and Chennai. [Hint: Use a ruler to find the distance between the cities on the map. Then, use the ratio given on the map to find the actual geographical distance.]
Answer

Measure the straight line joining the two dots, then multiply by the scale.

Ground distance = (map distance in cm) × 60 km

On the map printed in the book, a ruler gives about 2.4 cm from Bengaluru to Chennai and about 4.9 cm from Mangaluru to Chennai.

Pair of citiesMap distance× 60 kmActual straight-line distance
Bengaluru – Chennaiabout 2.4 cmabout 145 kmabout 290 km
Mangaluru – Chennaiabout 4.9 cmabout 295 kmabout 590 km
Why the two columns disagree: Look at the bottom-left corner of the map — it says “Map not to scale”. The picture has been reduced to fit the textbook page, so on the printed page 1 cm actually stands for about 120 km, not 60 km. Every answer read off this page therefore comes out about half the true distance. The method is correct; the printed scale is not. You can see the method is sound from the ratio: 4.9 ÷ 2.4 ≈ 2.05, and the real distances 590 ÷ 290 ≈ 2.03 — the map’s shape is faithful even though its scale label is not.
Check it yourself: Use the latitude–longitude grid printed on the map instead. Bengaluru and Chennai are about 2.7° of longitude apart near 13°N, and one degree of longitude there is about 108 km — giving roughly 290 km. Then measure the same two cities on an atlas map that carries its own scale and see the two answers agree.
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