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NCERT Solutions Ganita Prakash (Part 1) Chapter 7 –171Trairasika — Figure it Out

Book page 170 Updated on2026-09-05

Q1.
The Earth travels approximately 940 million kilometres around the Sun in a year. How many kilometres will it travel in a week?
Answer

About 1,80,76,923 km, that is roughly 1.81 crore kilometres in one week.

1 year ≈ 52 weeks
940 million km = 940 × 10⁶ = 94,00,00,000 km
52 : 940000000 :: 1 : x
x = 940000000 ÷ 52
x = 1,80,76,923 km (approximately)
Why this is a proportion: The Earth's orbital speed is very nearly steady, so distance and time rise together. Weeks and kilometres can therefore be paired as 52 : 940000000, and dividing by 52 gives the distance for one week.
Check it yourself: 52 × 1,80,76,923 = 93,99,99,996 km — back to 940 million, apart from the rounding. Using 365 days instead of 52 weeks gives 940000000 × 7 ÷ 365 ≈ 1,80,27,397 km; the small difference appears because a year is 52 weeks and one extra day.
Q2.
A mason is building a house in the shape shown in the diagram. He needs to construct both the outer walls and the inner wall that separates two rooms. To build a wall of 10-feet, he requires approximately 1450 bricks. How many bricks would he need to build the house? Assume all walls are of the same height and thickness.
Answer

15,660 bricks. First add up every foot of wall in the plan, then scale.

12 ft 15 ft 9 ft 9 ft 6 ft 9 × 12 15 × 12 6 × 9 inner wall = 12 ft
The plan: two rooms 9 ft and 15 ft wide share a 12 ft inner wall (red), and a 6 ft × 9 ft room hangs below. Every segment of the outline is a wall.
Top block (9 ft and 15 ft rooms, both 12 ft deep):
top edge 9 + 15 = 24 ft
bottom edge 9 + 15 = 24 ft
left side 12 ft, right side 12 ft
inner dividing wall 12 ft
Lower room (6 ft × 9 ft):
left 9 ft, right 9 ft, bottom 6 ft

Total = 24 + 24 + 12 + 12 + 12 + 9 + 9 + 6 = 108 ft
10 : 1450 :: 108 : x
10 × x = 108 × 1450
x = 156600 ÷ 10 = 15,660 bricks
Why the shared edge is counted once: The top edge of the small lower room is the same piece of masonry as part of the bottom edge of the big block — the mason lays those bricks once. Counting each rectangle's perimeter separately would charge for that wall twice and give 132 ft instead of 108 ft. Always trace the outline of the actual walls, then add the inner ones.
Tip: 108 ft is 10.8 lots of 10 ft, so the answer must be 10.8 × 1450. Doing it that way — 1450 + 4350 + 5800 + … — is easy to slip on; the cross-multiplication form 108 × 1450 ÷ 10 keeps the arithmetic in whole numbers.
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