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NCERT Solutions Ganita Prakash (Part 2) Chapter 3 Sections 3.2 Ratios in Maps · 3.3 Ratios with More than 2 Terms — In-text Questions

Book page 57 Updated on2026-09-05

Q1.
Try to find the distances between the same two pairs of cities with different maps that have different scales (ratios). Do they all give the same geographical distance, approximately?
Answer

Yes — every correctly drawn map gives roughly the same ground distance, even though the ruler readings are all different.

Scale (RF)1 cm stands forBengaluru–Chennai measuresGround distance
1 : 60,00,00060 kmabout 4.8 cmabout 290 km
1 : 1,20,00,000120 kmabout 2.4 cmabout 290 km
1 : 30,00,00030 kmabout 9.7 cmabout 290 km
Why it happens: The ground distance is fixed by geography, so it is the constant here. Map length × scale factor = ground distance. When the scale factor doubles, the length on paper halves — the two change by opposite factors and their product stays 290 km. This is the very first inverse relationship in the chapter, met before it is named in Section 3.6.
Tip: The answers will not match to the last kilometre. Ruler markings, the thickness of the printed dots, and the way a round Earth is flattened onto a flat sheet all add small errors. “Approximately the same” is the honest claim.
Q2.
Map Making Activity: Guide students to make a sketch of their classroom with an accurate scale (ratio of 1 : 50). They should mark the location of various objects in the classroom like the teacher’s desk, blackboard, fans and lights, according to scale. Students can use appropriate symbols to represent different objects like fans, lights, tables, chairs, and so on.
Answer

At 1 : 50, every 50 cm of the real classroom becomes 1 cm on your sheet.

1 cm on the sketch = 50 cm on the floor
So 1 m (= 100 cm) on the floor = 2 cm on the sketch

Measure the room and its objects with a metre scale or measuring tape, then divide every length by 50:

ObjectReal sizeSize on the sketch
Classroom floor8 m × 6 m16 cm × 12 cm
Blackboard3 m long6 cm long
Teacher’s desk1.5 m × 0.75 m3 cm × 1.5 cm
Student bench1 m × 0.3 m2 cm × 0.6 cm
Door0.9 m wide1.8 cm wide
  • Draw the outline of the room first, then place each object at its measured distance from a wall — position must be to scale as well as size.
  • A fan or a light has no useful floor size, so mark it with a symbol and explain the symbols in a legend, exactly as the map on page 56 explains its red dot as CITY.
  • Write “Scale 1 : 50” in a corner. A drawing without its scale cannot be measured by anyone else.
Why it happens: Every length shrinks by the same factor of 50, so all ratios inside the room survive. A desk twice as long as another is still twice as long on paper. That is what makes a scale drawing trustworthy — and it is the same reason the shapes on a map keep their form.
Q3.
Puneet has only 2 red chillies in his kitchen. But he wants to make spice mix powder that tastes the same as Viswanath’s spice mix powder. How much of the other ingredients should Puneet use to make his spice mix powder?
Answer

Halve every ingredient, because the chillies have been halved.

Viswanath — coriander : chillies : toor dal : fenugreek = 8 : 4 : 2 : 1
Puneet has 2 chillies, and 2 = 4 × ½
So multiply every term by ½:
8 × ½ = 4 spoons of coriander seeds
4 × ½ = 2 red chillies
2 × ½ = 1 spoon of toor dal
1 × ½ = 0.5 spoon of fenugreek seeds
4 : 2 : 1 : 0.5, and 8 : 4 : 2 : 1 :: 4 : 2 : 1 : 0.5
Why it happens: A four-term ratio is a statement about all the pairs at once. If only the chillies were halved, the coriander-to-chilli ratio would jump from 2 : 1 to 4 : 1 and the powder would taste quite different. Multiplying every term by the same factor is the only change that leaves all these internal ratios alone.
Check it yourself: 8/4 = 4/2 = 2/1 = 1/0.5 = 2. One common factor, four times over — that is the test the book states as a/p = b/q = c/r = d/s.
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