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Exercise 8.1 Page: 157

1. Find the ratio of:

(a) Rs 5 to 50 paise

Solution:-

We know that,

Rs 1 = 100 paise

Then,

Rs 5 = 5 × 100 = 500 paise

Now we have to find the ratio,

= 500/50

= 10/1

So, the required ratio is 10: 1.

(b) 15 kg to 210 g

Solution:-

We know that,

1 kg = 1000 g

Then,

15 kg = 15 × 1000 = 15000 g

Now we have to find the ratio,

= 15000/210

= 1500/21

= 500/7 … [∵divide both by 3]

So, the required ratio is 500: 7.

(c) 9 m to 27 cm

Solution:-

We know that,

1 m = 100 cm

Then,

9 m = 9 × 100 = 900 cm

Now we have to find the ratio,

= 900/27

= 100/3 … [∵divide both by 9]

So, the required ratio is 100: 3.

(d) 30 days to 36 hours

Solution:-

We know that,

1 day = 24 hours

Then,

30 days = 30 × 24 = 720 hours

Now we have to find the ratio,

= 720/36

= 20/1 … [∵divide both by 36]

So, 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:-

From the question it is given that,

Number of computer required for 6 students = 3

So, number of computer required for 1 student = (3/6)

= ½

So, number of computer required for 24 students = 24 × ½

= 24/2

= 12

∴Number of computer required for 24 students is 12 computers.

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) From the question, it is given that,

Population of Rajasthan = 570 lakh

Area of Rajasthan = 3 lakh Km2

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

= 190 people per km2

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.