1. Find the ratio of:

(a) ₹ 5 to 50 paise

Solution:

First, we convert ₹ 5 to paise to find the ratio,

We know that,

₹ 1 = 100 paise

So,

₹ 5 = 5 × 100

      = 500 paise

According to the question we have to find the ratio,

= 500/50

= 10/1

Hence, the required ratio is 10: 1.

(b) 15 kg to 210 g

Solution:

First, we convert 15 Kg in g,

We know that,

1 kg = 1000 g

So,

15 kg = 15 × 1000 = 15000 g

According to the question we have to find the ratio,

= 15000/210

= 1500/21

Dividing both by 3

= 500/7

Hence, the required ratio is 500: 7.

(c) 9 m to 27 cm

Solution:

First, we convert m 9 m into cm,

We know that,

1 m = 100 cm

So,

9 m = 9 × 100 = 900 cm

According to the question we have to find the ratio,

= 900/27

Dividing both by 9

= 100/3

Hence, the required ratio is 100: 3.

(d) 30 days to 36 hours

Solution:

First, we convert 30 days into hours to find the ratio,

We know that,

1 day = 24 hours

So,

30 days = 30 × 24 = 720 hours

According to the question we have to find the ratio,

= 720/36

Dividing both by 36

= 20/1

Hence, the required ratio is 20: 1.

2. In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?

Solution:

Given,

Total number of computers required for 6 students = 3

So, the total number of computers required for 1 student = (3/6)

                                                                                      = ½

Now, total number of computer required for 24 students = 24 × ½

                                                                                            = 24/2

                                                                                            = 12

Hence, the total number of computers required for 24 students is 12.

3. Population of Rajasthan = 570 lakhs and population of UP = 1660 lakhs.

Area of Rajasthan = 3 lakh km² and area of UP = 2 lakh km².

(i) How many people are there per km² in both these States?

(ii) Which State is less populated?

Solution:

(i) Given,

Population of Rajasthan = 570 lakh

Area of Rajasthan = 3 lakh Km²

So, population of Rajasthan in 1 km² area = (570 lakh)/ (3 lakh km²)

                                                                    = 190 people per km²

Now,

Population of UP = 1660 Lakh

Area of UP = 2 Lakh km²

Then, population of UP in 1 lakh km² area = (1660 lakh)/ (2 lakh km²)

                                                                    = 830 people per km²

(ii) By comparing the two states Rajasthan is the less populated state.