Exercise 3.2 - Chapter 3 Ratio and Proportion Term 1 6th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Ex $3.2$
Question 1 .
Fill in the blanks of the given equivalent ratios.
(i) $3: 5=9$ :
(ii) $4: 5=$
(iii) 6 :
Solution:
(i) 15
Hint: $\frac{3}{5}=\frac{3 \times 3}{5 \times 3}=\frac{9}{15}$
(ii) 8
Hint: $\frac{4}{5}=\frac{4 \times 2}{5 \times 2}=\frac{8}{10}$
(iii) 12
Hint: $\frac{1}{2}=\frac{1 \times 6}{2 \times 6}=\frac{6}{12}$

Question $2 .$
Complete the Table:

Solution:

Question $3 .$
Say True or False.
(i) $5: 7$ is equivalent to $21: 15$.
(ii) If 40 is divided in the ratio $3: 2$, then the larger part is $24 .$
Solution:
(i) False
(ii) True

Question $4 .$
Give two equivalent ratios for each of the following.
(i) $3: 2$
(ii) $1: 6$
(iii) $5: 4$
Solution:
(i) $3: 2$
$\frac{3}{2} \times \frac{2}{2}=\frac{6}{4}=6: 4$ $\frac{3}{2} \times \frac{3}{3}=\frac{9}{6}=9: 6 \quad 6: 4$ and $9: 6$ are equivalent to $3: 2$
(ii) $1: 6$
Equivalent Ratios of $1: 6$ are
$\begin{aligned}
&\frac{1}{6} \times \frac{2}{2}=\frac{2}{12}=2: 12 \\
&\frac{1}{6} \times \frac{3}{3}=\frac{3}{18}=3: 18
\end{aligned}$
$2: 12$ and $3: 18$ are equivalent to $1: 6$
(iii) $5: 4$
$\begin{aligned}
&\frac{5}{4} \times \frac{2}{2}=\frac{10}{8}=10: 8 \\
&\frac{5}{4} \times \frac{3}{3}=\frac{15}{12}=15: 12
\end{aligned}$
Equivalent ratios of $5: 4$ are $10: 8$ and $15: 12$

Question $5 .$
Which of the two ratios is larger?
(i) $4: 5$ or $8: 15$
(ii) $3: 4$ or $7: 8$
(iii) $1: 2$ or $2: 1$
Solution:
(i) $4: 5=\frac{4}{5} \times \frac{3}{3}=\frac{12}{15}$
$8: 15=\frac{8}{15}$
Here $\frac{12}{15}$ larger than $\frac{8}{15}$ and $4: 5$ is larger than $8: 15$
(ii) $3: 4$ or $7: 8$
$3: 4=\frac{3}{4} \times \frac{2}{2}=\frac{6}{8}$

$7: 8=\frac{7}{8}$
Here $\frac{7}{8}$ longer than $\frac{6}{8}$ $\therefore 7: 8$ longer than $3: 4$
(iii) $1: 2$ or $2: 1$
$1: 2=\frac{1}{2}$ $2: 1=\frac{2}{1} \times \frac{2}{2}=\frac{4}{2}$
Here $\frac{4}{2}$ longer than $\frac{1}{2}$
$\therefore 2: 1$ larger than $1: 2$
 

Question 6 .
Divide the numbers given below in the required ratio.
(i) 20 in the ratio $3: 2$
(ii) 27 in the ratio $4: 5$
(iii) 40 in the ratio $6: 14$
Solution:
(i) Ratio $=3: 2$
Sum of the ratio $=3+2=5$
5 parts $=20$
1 part $=\frac{20}{5}$
$=4$
3 parts $=3 \times 4=12$

2 parts $=2 \times 4=8$
20 can be divided in the form as 12,8 .
(ii) Ratio $=4: 5$
Sum of the ratio $=4+5=9$
9 parts $=27$
1 part $=\frac{27}{9}=3$
4 parts $=4 \times 3=12$
5 parts $=5 \times 3=15$
27 can be divided in the form as 12,15 .
(iii) 40 in the ratio $6: 14$
Ratio $=6: 14$
Sum of the ratio $=6+14=20$
20 parts $=40$
1 part $=\frac{40}{20}=2$
6 parts $=2 \times 6=12$
14 parts $=2 \times 14=28$
40 can be divided in the form as 12,28 .

Question 7 .
In a family, the amount spent in a month for buying Provisions and Vegetables are in the ratio $3: 2$.
If the allotted amount is ₹ 4000 , then what will be the amount spent for
(i) Provisions and
(ii) Vegetables?
Solution:
Dividing the total amount ₹ 4000 into $3+2=5$ equal parts then
(i) For Provisions:
3 out of 5 parts are spent for provisions and 2 out of 5 parts for vegetables.
$4000 \times \frac{3}{5}=2100$ for provisions
(ii) For vegetables:
$4000 \times \frac{2}{5}=1600$ for Vegetables.
₹ 2400 spend on provisions and ₹ 1600 spend on Vegetables.

Question 8 .
A line segment $63 \mathrm{~cm}$ long is to be divided into two parts in the ratio $3: 4$. Find the length of each part.
Solution:
Total length $=63 \mathrm{~cm}$ Ratio $=3: 4$
Sum of the ratio $=3+4=7$
7 parts $=63 \mathrm{~cm}$
1 part $=\frac{63}{7}=9 \mathrm{~cm}$
3 parts $=3 \times 9 \mathrm{~cm}=27 \mathrm{~cm}$
4 parts $=4 \times 9 \mathrm{~cm}=36 \mathrm{~cm}$
$\therefore 63 \mathrm{~cm}$ can be divided into the parts as $27 \mathrm{~cm}$ and $36 \mathrm{~cm}$.
 

Objective Type Questions
Question $9 .$
If $2: 3$ and $4:$ or equivalent ratios, then the missing term is
(a) 6
(b) 2
(v) 4
(d) 3
Solution:
(a) 6
Hint: $\frac{2}{3}=\frac{2 \times 2}{3 \times 2}=\frac{4}{6}$

Question $10 .$
An equivalent ratio of $4: 7$ is
(a) $1: 3$
(b) $8: 15$
(c) $14: 8$
(d) $12: 21$
Solution:
(d) $12: 21$
 

Question $11 .$
Which is not an equivalent ratio of $\frac{16}{24}$ ?
(a) $\frac{6}{9}$
(b) $\frac{12}{18}$
(c) $\frac{10}{15}$
(d) $\frac{20}{28}$
Solution:
(d) $\frac{20}{28}$
Hint: $\frac{16}{24}=\frac{8 \times 2}{8 \times 3}=\frac{2}{3}$
 

Question 12 .
If Rs 1600 is divided
(a) Rs 480
(b) Rs 800

(c) Rs 1000
(d) Rs 200
Solution:
(c) Rs 1000