Sum of the ratios = 3 + 2 = 5
Semi-perimeter = Length + Breadth = 50 m
\(\therefore\) Length = \(\frac { 3 }{ 5 } \times 50\) = 30 m
Breadth = \(\frac { 2 }{ 5 } \times 50\) = 20 m

2 : 15

\(3:8=\frac{3}{8}=\frac{3\times2}{8\times2}=\frac{6}{16},3:8=\frac{3}{8}=\frac{3\times3}{8\times3}=\frac{9}{24}\)
Hence, two equivalent ratios of 3: 8 are 6: 16 and 9: 24.

32,48,70 and 210 are not in proportion.

Since, two quantities are not in the same unit.
Firstly, we have to convert them into same unit.
We know that 1 m= 100 cm \(\Rightarrow\) 1.2 m= 1.2 x 100 cm= 120 cm
\(\therefore\) Ratio of 80 cm to 1.2 m, i.e. 80 cm to 120 cm \(=\frac{80}{120}=\frac{2}{3}\),hence the required ratio is 2 : 3.

\(\frac { 40 }{ 5 } =\frac { 8 }{ 1 } \)
\(\frac { 42 }{ 6 } =\frac { 7 }{ 1 } \)
\(\because\) 8 > 7
\(\therefore\) First shopkeeper is costlier
\(\therefore\) Tomatoes must be purchased from the second shopkeeper.
The comparison by taking difference will not help him decide as the weights of tomatoes  purchased from the two shopkeepers are different.
 

Ratio of sides of triangle = 2 : 3 : 5
Total perimeter = 70
Total of the ratio of sides = 2 + 3 + 5 =10
\(\therefore\) Length of the longest side = \(70\times\frac{5}{10}=35\ cm\)

Runs made by Anish in 6 overs = 42
\(\therefore\) Runs made by Anish in 1 over \(=\frac{42}{6}=7\)
Runs made by Anup in 7 overs = 63
\(\therefore\) runs made by Anup in 1 over \(=\frac{63}{7}=9\)
\(\because\) 9>7
Hence, Anup made more runs per over.

8:9

Given, number of holidays in one year = 73
We know that, number of days in one year = 365
\(\therefore\) Ratio of number of holidays to the number of days in one year \(=\frac {Number\ of\ holidays}{Total\ number\ of\ days}=\frac {73}{365}\)
\(=\frac{73\div73}{365\div73}=\frac{1}{5}=1:5\) [\(\because\)HCF of 73 and 365 = 73]
Hence, the required ratio is 1 : 5.

Given, Ravi earns in a year = Rs.360000 and Ravi paid income tax in a year = Rs.24000
(a) Ratio of income to the income tax paid
paid = 360000 : 24000
= 360: 24 [dividing by 1000 in both ratios]
= 15 :1 [dividing by 24 in both ratios]
Hence, the ratio of income to income tax is 15: 1.
(b) After paying income tax remaining income
= Total income -Income tax
= 360000 - 24000 = Rs.336000
\(\therefore\)  Ratio of income tax to income after paying income tax
= 24000 : 336000
= 24: 336 [dividing by 1000 in both ratios]
=1 :14 [dividing by 14 in both ratios]
Hence, the ratio of income tax to afer paying income tax is 1 : 14.

255 m

Given, total number of students in a class = 30
Number of students who like football = 6
Number of students wholike cricket = 12
Then, number of students who like tennis
= Total number of students - (Number of students who like football + Number of students who like cricket)
= 30 - (6 + 12) = 30 -18 = 12
(a) Ratio of number of students liking football to number of students liking tennis \(=\frac{Number\ of\ students\ who\ like\ football}{Number\ of\ students\ who\ like\ tennis}\)
\(=\frac{6}{12}=\frac{6\div6}{12\div6}=\frac{1}{2}=1:2\) [ \(\because\)HCF of 6 and 12 = 6]
(b) Ratio of number of students liking cricket to total number of students \(=\frac{Number\ of\ students\ who\ like\ cricket}{Total\ number\ of\ students}=\frac{12}{30}\)
\(=\frac{12\div6}{30\div6}=\frac{2}{5}\) [\(\because\)HCF of 12 and 30 = 6]