(a) Rs 5 to 50 paise

1 rupee = 100 paise

5 rupee = 500 paise

$\frac{\mathrm{Rs} 5}{50 \mathrm{Paise}}=\frac{500}{50}=\frac{10}{1}$

Hence, the required ratio is 10:1.

(b) 15 kg to 210 g

1 kg = 1000 g

15 kg = 15000 g

$\Rightarrow \frac{15 Kg}{210 g}=\frac{15000}{210}=\frac{500}{7}$

Hence, the required ratio is 500:7.

(c) 9 m to 27 cm

1 m = 100 cm

9 m = 900 cm

$\Rightarrow \frac{9 cm}{27 cm}=\frac{900}{27}=\frac{100}{3}$

Hence, the required ratio is 100:3.

(d) 30 days to 36 hours

1 days = 24 hrs

30 days = 24 × 30 = 720 hrs

$\Rightarrow \frac{30 days}{36 hrs}=\frac{720}{36}=\frac{20}{1}$

Hence, the required ratio is 20:1.

For 6 students, number of computers required = 3

∴ For 1 student, number of computers required =$\frac{3}{6}=\frac{1}{2}$

∴ For 24 students, number of computers required =$24\times \frac{1}{2}$= 12 Hence, 12 computers are required for 24 students.

(i) Population of Rajasthan in 3 km² area = 570 lakh

Population of Rajasthan in 1 km² area =$\frac{570}{3}=190 \mathrm{lakh}$

Population of U.P in 2 km² area = 1660 lakh

Population of U.P in 1 km² area =$\frac{1660}{2}$ = 830 lakh

(ii) It can be observed that population per km² area is lesser for Rajasthan. Therefore, Rajasthan is less populated.

(a)

$$\begin{gathered} \frac{1}{8}=\frac{1}{8}\times \frac{100}{100} \\ =\frac{1}{8}\times 100\% \\ =12.5\% \end{gathered}$$

(b) $\frac{5}{4}$

$$\begin{gathered} \frac{5}{4}=\frac{5}{4}\times \frac{100}{100} \\ =\frac{500}{4}\%=125\% \end{gathered}$$

(c) $\frac{3}{40}$

$$\begin{gathered} \frac{3}{40}=\frac{3}{40}\times \frac{100}{100} \\ =\frac{300}{40}\%=7.5\% \end{gathered}$$

(d) $\frac{2}{7}$

$\frac{2}{7}=\frac{2}{7}\times \frac{100}{100}=\frac{200}{7}\%=28\frac{4}{7}\%$