NCERT Solutions for Class 8 Maths Ganita Prakash Chapter 7 — Figure it Out (Pages 170–171)#
The rule of three: if $a : b :: c : x$, the missing term is found by multiplying $b$ by the same factor that changes $a$ into $c$:
$$x = b \times \dfrac{c}{a}$$1. The Earth travels approximately 940 million kilometres around the Sun in a year. How many kilometres will it travel in a week? #
Solution
A year has about 52 weeks, and the distance is proportional to the time:
$$52 : 940000000 :: 1 : x$$$$x = 940000000 \times \dfrac{1}{52}$$$$x = 18076923 \text{ (about)}$$
∴ The Earth travels about 1,80,76,923 km (roughly 18 million km) in a week.
(Using a year of 365 days, a week is $\dfrac{7}{365}$ of a year, which gives about 1,80,27,397 km. Both answers are about 18 million km.)
2. 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. #
Solution
Total length of walls. We add every wall in the plan:
| Walls | Length (ft) |
|---|---|
| Top: $9 + 15$ | 24 |
| Left and right sides: $12 + 12$ | 24 |
| Inner wall between Room 1 and Room 2 | 12 |
| Bottom of Room 1 | 9 |
| Bottom of Room 2 (including the wall it shares with Room 3) | 15 |
| Sides of Room 3: $9 + 9$ | 18 |
| Bottom of Room 3 | 6 |
| Total | 108 |
Number of bricks. Bricks are proportional to the length of wall:
$$10 : 1450 :: 108 : x$$$$x = 1450 \times \dfrac{108}{10}$$$$x = 145 \times 108$$
$$x = 15660$$
∴ The mason needs about 15,660 bricks.