NCERT Solutions Class 8 Maths Ganita Prakash Chapter 7 Proportional Reasoning-1 on Padhaiwise

NCERT Solutions for Class 8 Maths Ganita Prakash Chapter 7 Proportional Reasoning-1 Figure it Out Page 165

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 8 Maths Ganita Prakash Chapter 7 — Figure it Out (Pages 165–167)#

Two ratios $a : b$ and $c : d$ are proportional, written $a : b :: c : d$, when both terms of one are multiplied by the same number to give the other. An easy test: write both in their simplest form and compare, or check that $a \times d = b \times c$.

NCERT Solutions for Class 8 Maths Ganita Prakash Chapter 7 Proportional Reasoning-1 Figure it Out Page 170

Mon, 01 Jan 0001 00:00:00 +0000

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:

NCERT Solutions for Class 8 Maths Ganita Prakash Chapter 7 Proportional Reasoning-1 Figure it Out Page 175

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 8 Maths Ganita Prakash Chapter 7 — Figure it Out (Page 175)#

To divide a quantity $x$ in the ratio $m : n$, split it into $m + n$ equal parts:

first share $= \dfrac{m}{m + n} \times x$
second share $= \dfrac{n}{m + n} \times x$

1. Divide ₹4,500 into two parts in the ratio 2 : 3. #

Solution

There are $2 + 3 = 5$ equal parts.

NCERT Solutions for Class 8 Maths Ganita Prakash Chapter 7 Proportional Reasoning-1 Figure it Out Page 176

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 8 Maths Ganita Prakash Chapter 7 — Figure it Out (Pages 176–177)#

Unit conversions used here: 1 acre = 43,560 sq ft, 1 litre = 1000 mL, 1 tonne = 1000 kg, 1 kg = 1000 g.

1. Anagh mixes 600 mL of orange juice with 900 mL of apple juice to make a fruit drink. Write the ratio of orange juice to apple juice in its simplest form. #

Solution

The HCF of 600 and 900 is 300: