Important Questions: Comparing Quantities | Mathematics (Maths) Class 7 PDF Download

Q1: Find the ratio of
(a) Rs. 5 to 50 paise
Ans:
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
Ans:
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
Ans:
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
Ans:
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.

Q2: In a computer lab, there are three computers for every six students. How many computers will be needed if there are 24 students?
Answer:
From the above question, it is given that,
Then, Number of computers required for six students = is 3
So, the number of computers required for one student = (3/6)
= ½
Hence, the Number of computers required for the 24 students = 24 × ½
= 24/2
= 12
Therefore, the Number of computers required for 24 students is 12 computers.

Q3: It is given that the Population of Rajasthan = is 570 lakhs, and the population of UP = is 1660 lakhs.
The area of Rajasthan is = 3 lakh km sq, and area of UP = 2 lakh km sq.
(a) How many people are present per km sq in both these States?
(b) Which of the above State is less populated?
Ans:
(a) From the above question, it is given that,
The population of the state Rajasthan = 570 lakh
Area of the state Rajasthan = 3 lakh Km2
Then, the final population of the state Rajasthan in 1 km sq area = (570 lakh)/ (3 lakh km2)
= 190 people are there per km2
The population of UP is = 1660 Lakh
Area of UP is = 2 Lakh km2
Then, the population of UP in 1 lakh km sq area = (1660 lakh)/ (2 lakh km2)
= 830 people per km sq
(ii) By comparing the two states, Rajasthan was found to be the less populated state.

Q4: Convert the given fractional numbers given below to percent.
(i) 1/8
Ans:
In order to convert a fraction into percentage, multiply it by the fraction of 100 and then put the percent sign %.
= (1/8) × 100 %
= 100/8 %
= 12.5%

(ii) 5/4
Ans: In order to convert a fraction into percentage, multiply the fraction by 100 and then put the per cent sign %.
= (5/4) × 100 %
= 500/4 %
= 125%

(iii) 3/40
Ans: In order to convert a fraction into percentage, multiply the fraction by 100 and then put the percent sign %.
= (3/40) × 100 %
= 300/40 %
= 30/4 %
= 7.5%

Q5: Convert the following given decimal fraction to percent.
(i) 0.65
Ans: Firstly we have to remove the decimal point,
= 65/100
Now,
Multiply it by 100 and then put the percent sign %.
We have,
= (65/100) × 100
= 65%

(ii) 2.1
Ans: Firstly we have to remove the decimal point,
= 21/10
Now,
Multiply it by 100 and then put the percent sign %.
We have,
= (21/10) × 100
=210%

(iii) 0.02
Ans: Firstly we have to remove the decimal point,
= 2/100
Now,
Multiply it by 100 and put the percent sign %.
We have,
= (2/100) × 100
= 2%

(iv) 12.35
Ans: Firstly we have to remove the decimal point,
= 1235/100
Now,
Multiply it by 100 and put the percent sign %.
We have,
= (1235/100) × 100)
= 1235%

Q6: Find: (a) 15% of 250
Ans: We have,
= (15/100) × 250
= (15/10) × 25
= (15/2) × 5
= (75/2)
= 37.5

(b) 1% of 1 hour
Ans: We know that 1 hour = 60 minutes
Then,
1% of 60 minutes
1 minute = 60 seconds
60 minutes = 60 × 60 = 3600 seconds
Now,
1% of 3600 seconds
= (1/100) × 3600
= 1 × 36
= 36 seconds

(c) 20% of Rs. 2500
Ans:
We have,
= (20/100) × 2500
= 20 × 25
= Rs. 500

(d) 75% of 1 kg
Ans:
We know that 1 kg = 1000 g
Then,
75% of 1000 g
= (75/100) × 1000
= 75 × 10
= 750 g

Q7: Find the whole quantity if
(i) 5% of it is 600
Ans:
Let us assume that the whole quantity is x,
Then,
(5/100) × (x) = 600
X = 600 × (100/5)
X = 60000/5
X = 12000

(ii) 12% of it is Rs. 1080.
Ans:
Let us assume that the whole quantity is x,
Now,
(12/100) × (x) = 1080
X = 1080 × (100/12)
X = 540 × (100/6)
X = 90 × 100
X = Rs. 9000

(iii) 40% of it is 500 km
Ans:
Let us assume that the whole quantity is x,
Now,
(40/100) × (x) = 500
X = 500 × (100/40)
X = 500 × (10/4)
X = 500 × 2.5
X = 1250 km

(iv) 70% of it is 14 minutes
Ans: Let us assume the whole quantity is x,
Now,
(70/100) × (x) = 14
X = 14 × (100/70)
X = 14 × (10/7)
X = 20 minutes

(v) 8% of it is 40 litres
Ans: Let us assume the whole quantity is x,
Now,
(8/100) × (x) = 40
X = 40 × (100/8)
X = 40 × (100/8)
X = 40 × 12.5
X = 500 litres

Q8: Convert the given percent to decimal fractions and also convert these fractions in simplest forms:
(i) 25%
Ans: Firstly convert the given above percentage into a fraction and then convert the fraction into decimal form.
= (25/100)
= ¼
= 0.25

(ii) 150%
Ans: Firstly convert the given above percentage into a fraction and then convert the fraction into decimal form.
= (150/100)
= 3/2
= 1.5

(iii) 20%
Ans: Firstly convert the given above percentage into a fraction and then convert the fraction into decimal form.
= (20/100)
= 1/5
= 0.2

(iv) 5%
Ans: First, convert the above-given percentage into a fraction and then put these fractions into decimal form.
= (5/100)
= 1/20
= 0.05

Q9: In a city, 30% of the public are females, 40% of them are males, and the remaining are children. What percent of them are children?
Ans: From the above question, it is given that
Percentage of females in the city =30%
Percentage of males in the city = 40%
Total percentage of both male and female = 40% + 30%
= 70%
Now we will have to find the percentage of children present in the city = 100 – 70
= 30%
So, 30% are children.

Q10: Out of 15,000 voters in a constituency, 60% of people voted. Find the percentage of voters who didn’t vote. Now find out how many of them actually did not vote.
Ans:
From the above question, it is given that
Total Number of voters present in the constituency = 15000
The percentage of people that voted in the election is = 60%
The percentage of people who did not vote in the election is = 100 – 60
= 40%
The total number of voters who did not vote in the election is = 40% of 15000
= (40/100) × 15000
= 0.4 × 15000
= 6000 voters
∴ Six thousand voters did not vote.

Q11: Meeta saves Rs. 4000 from her salary. Suppose this is 10% of her salary. Then What is her total salary?
Ans:
Let us assume that
Meeta’s salary be Rs. x,
Now,
10% of Rs. x = Rs. 4000
(10/100) × (x) = 4000
X = 4000 × (100/10)
X = 4000 × 10
X = Rs. 40000
Hence Meeta’s salary is Rs. 40000.

Q12: A local cricket team played around 20 matches in one season. They won 25% of the matches. Hence how many matches did they win?
Ans:
From the above question, it is given that the
Total matches played by the local team = 20
Percentage of matches won by these local teams = 25%
Now,
The number of matches won by the team is = 25% of the 20
= (25/100) × 20
= 25/5
= 5 matches.
Hence, The local team won 5 matches out of 20 matches.

Q13: Tell the profit or loss in the following transactions. Also, find the profit per cent or the loss per cent in each of the below cases.
(i) Gardening shears bought for Rs. 250 and sold for Rs. 325.
Ans: From the above question, it is given that
The cost price of the gardening shears = Rs. 250
The selling price of the gardening shears = Rs. 325
Since (SP) > (CP), hence there is a profit.
Profit is = (SP) – (CP)
= Rs. (325 – 250)
= Rs. 75
Profit % = {(Profit/CP) × 100}
= {(75/250) × 100}
= {7500/250}
= 750/25
= 30%

(ii) A refrigerator bought for Rs. 12,000 and sold at Rs. 13,500.
Ans:
From the above question, it is given that the
The cost price of the refrigerator is = Rs. 12000
The selling price of the refrigerator is = Rs. 13500
Since (SP) > (CP), hence there is a profit
Profit = (SP) – (CP)
= Rs. (13500 – 12000)
= Rs. 1500
Profit % = {(Profit/CP) × 100}
= {(1500/12000) × 100}
= {150000/12000}
= 150/12
= 12.5%

(iii) A cupboard bought for Rs. 2,500 and sold at Rs. 3,000.
Ans:
From the above question, it is given that
The cost price of the cupboard is = Rs. 2500
The selling price of the cupboard is = Rs. 3000
Since (SP) > (CP), hence there is a profit.
Profit = (SP) – (CP)
= Rs. (3000 – 2500)
= Rs. 500
Profit % = {(Profit/CP) × 100}
= {(500/2500) × 100}
= {50000/2500}
= 500/25
= 20%

(iv) A skirt bought for Rs. 250 and sold at Rs. 150.
Ans: Since (SP) < (CP), hence there is a loss.
Loss is = (CP) – (SP)
= Rs. (250 – 150)
= Rs. 100
Loss % = {(Loss/CP) × 100}
= {(100/250) × 100}
= {10000/250}
= 40%

Q14: Convert each part of the ratio given below to a percentage:
(i) 3: 1
Ans:
We have to find the total parts by adding the given ratio = 3 + 1 = 4
1st part = ¾ = (¾) × 100 %
= 3 × 25%
= 75%
2nd part = ¼ = (¼) × 100%
= 1 × 25
= 25%

(ii) 2: 3: 5
Ans: We have to find the total parts by adding the given ratio as = 2 + 3 + 5 = 10
1st part = 2/10 = (2/10) × 100 %
= 2 × 10%
= 20%
2nd part = 3/10 = (3/10) × 100%
= 3 × 10
= 30%
3rd part = 5/10 = (5/10) × 100%
= 5 × 10
= 50%

(iii) 1:4
Ans: We have to find the total parts by adding the given ratio = 1 + 4 = 5
1st part = (1/5) = (1/5) × 100 %
= 1 × 20%
= 20%
2nd part = (4/5) = (4/5) × 100%
= 4 × 20
= 80%

(iv) 1: 2: 5
Ans:
We have to find the total parts by adding the given ratio as = 1 + 2 + 5 = 8
1st part = 1/8 = (1/8) × 100 %
= (100/8) %
= 12.5%
2nd part = 2/8 = (2/8) × 100%
= (200/8)
= 25%
3rd part = 5/8 = (5/8) × 100%
= (500/8)= 62.5%

Q15: The population of a city gets decreases from 25,000 to 24,500. Find the percentage decrease.
Ans:
From the above question, it is given that.
The Initial population of the city is = 25000
The final population of the city is = 24500
Population decrease is equal to = Initial population – Final population
= 25000 – 24500
= 500
Now,
Percentage decrease in the population = (population decrease/Initial population) × 100
= (500/25000) × 100
= (50000/25000)
= 50/25
= 2%