Gujarat Board GSEB Textbook Solutions Class 7 Maths Chapter 8 Comparing Quantities Ex 8.1 Textbook Questions and Answers.
Gujarat Board Textbook Solutions Class 7 Maths Chapter 8 Comparing Quantities Ex 8.1
Question 1.
Find the ratio of:
(a) ₹ 5 to 50 paise
(b) 15 kg to 210 g
(c) 9 m to 27 cm
(d) 30 days to 36 hours
Solution:
(a) ₹ 5 to 50 paise:
∵ ₹ 5 = 5 x 100 paise = 500 paise
∵ ₹ 5 to 50 paise = ₹ 5 : 50 paise
= 500 paise : 50 paise
= 500 : 50 [∵ HCF of 50 and 500 is 50]
= \(\frac { 500 }{ 50 }\) : \(\frac { 50 }{ 50 }\)
= 10 : 1
(b) 15 kg to 210 g:
∵ 15 kg = 15 x 1000 g = 15000 g
∴ 15 kg to 210 g= 15 kg : 210 g
= 15000 g : 210 g
= 15000 : 210 [∵ HCF of 15000 and 210 is 30]
= \(\frac { 1500 }{ 30 }\) \(\frac { 210 }{ 30 }\)
= 500 : 7
(c) 9 m to 27 cm:
∵ 9 m = 9 x 100 cm = 900 cm
∴ 9 m to 27 cm = 9 m : 27 cm
= 900 cm : 27 cm
= 900 : 27
[∵ HCF of 900 and 27 is 9]
= \(\frac { 900 }{ 9 }\) = \(\frac { 27 }{ 9 }\)
(d) 30 days to 36 hours:
∵ 30 days = 30 x 24 hours
= 720 hours
∴ 30 days to 36 hours = 30 days : 36 hours
= 720 hours : 36 hours
= 720 : 36
[∵ HCF of 720 and 36 is 36]
= \(\frac { 720 }{ 36 }\) = \(\frac { 36 }{ 36 }\)
Question 2.
In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?
Solution:
First method
∵ Number of computers for 6 students = 3
Number of computers for 1 student = \(\frac { 3 }{ 6 }\)
∴ Number of computers for 24 students
= \(\frac { 3 }{ 6 }\) x 24 = 3 x 4 = 12
Thus, the required number of computers =12 Second method
Let the required number of computers be x
∴ 3 : x = 6 : 24 ⇒ \(\frac { 3 }{ x }\) = \(\frac { 6 }{ 24 }\)
or 3 x 24 = 6 × x
∴ x = \(\frac { 3×24 }{ 6 }\)
Thus, the required number of computers = 12.
Question 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) For Rajasthan
Population = 570 lakhs
Area = 3 lakh km²
∴ Population per km = lakh/km²
= 190 lakh per km²
i.e. In Rajasthan, there are 190 lakhs people per km².
For UP
Population = 1660 lakhs
Area = 2 lakh km²
∴ Population per km² = \(\frac { 1660 }{ 2 }\) lakh per km²
= 830 lakh per km²
i.e. In UP, there are 830 lakhs people per km².
(ii) ∵ 190 lakhs <830 lakhs.
∴ Rajasthan is less populated state.