NCERT Exemplar Solutions Class 7 Maths Solutions Chapter 7 Comparing Quantities

Directions: In questions 1 to 23, there are four options, out of which one is correct. Write the correct one.

Question 1.
20% of 700 m is
(a) 560 m
(b) 70 m
(c) 210 m
(d) 140 m
Solution:
(d) 20% of 700 m
=(20100×700)m=140m

Question 2.
Gayathri’s income is ₹ 1,60,000 per year. She pays 15% of this as house rent and 10% of the remainder on her child’s education. The money left with her is
(a) ₹ 136000
(b) ₹ 120000
(c) ₹ 122400
(d) ₹ 14000
Solution:
(c) Gayatri’s income = ₹ 160000
House rent =15100×160000= ₹ 24000
Remaining amount – 160000 – 24000 = ₹ 136000
Expenditure on child’s education
=10100×136000
= ₹ 13600
∴ Money left with her
= ₹ (160000 – 24000 – 13600)
= ₹ (160000 – 37600) = ₹ 122400

Question 3.
The ratio of Fatima’s income to her savings is 4 : 1. The percentage of money saved by her
(a) 20%
(b) 25%
(c) 40%
(d) 80%
Solution:
(b) Let Fatima’s income be 4x and savings be x.
Savings percentage =x4x×100=25%

Question 4.
0.07 is equal to
(a) 70%
(c) 0.7%
(b) 7%
(d) 0.07%
Solution:
(b)
0.07=7100=7%

Question 7.
5.2 is equal to
(a) 52%
(b) 5.2%
(c) 520%
(d) 0.52%
Solution:
(c) 5.2=5210×1010=520100=520%

Question 8.
The ratio 3 : 8 is equal to
(a) 3.75%
(b) 37.5%
(c) 0.375%
(d) 267%
Solution:
(b) 38=0.375=37.5100=37.5%

Question 9.
225% is equal to
(a) 9 : 4
(b) 4 : 9
(c) 3 : 2
(d) 2 : 3
Solution:
(a) 225%=225100=94=9:4

Question 30.
A _______ with its denominator 100 is called a per cent.
Solution:
Fraction: A fraction with its denominator 100 is called a percent.

Question 31.
15 kg is ________ % of 50 kg.
Solution:
30: Let 15 kg is x% of 50 kg
∴ x100×50=15
⇒ x = 15 × 2 = 30

 

Question 33.
In a class of 50 students, 8 % were absent on one day. The number of students present on that day was _________
Solution:
46: Total number of students = 50
Number of absent students =8100×50=4
∴ Number of present students = 50 – 4 = 46

Question 37.
John sells a bat for ₹ 75 and suffers a loss of ₹ 8. The cost price of the bat is _________
Solution:
₹ 83: S.P. of bat = ₹ 75
Loss = ₹ 8
∴ C.P. = 75 + 8 = ₹ 83

Question 39.
Mohini bought a cow for ₹ 9000 and sold it at a loss of ₹ 900. The selling price of the cow is _______
Solution:
8100: C.P. of the cow = ₹ 9000
Loss = ₹ 900
∴ S.P. of the cow = 9000 – 900 = ₹ 8100

Question 54.
To convert a fraction into a percent, we _______ it by 100.
Solution:
Multiply: To convert a fraction into a percent, we multiply it by 100.

Question 55.
To convert a decimal into a percent, we shift the decimal point two places to the _________
Solution:
Right: To convert a decimal into a percent, we shift the decimal point two places to the right

Directions: In questions 58 and 59, copy each number line.

Fill in the blanks so that each mark on the number line is labelled with a per cent, a fraction and a decimal. Write all fractions in lowest terms.

Question 61.
When an improper fraction is converted into percentage then the answer can also be less than 100.
Solution:
False
When an improper fraction is converted into percentage then the answer always greater than 100

Question 62.
8 hours is 50% of 4 days.
Solution:
False
1 day = 24 hours
∴ 4 days = 24 × 4 = 96 hours
Now, 50% of 96 hours =50100×96=48 hours

Question 70.
250 cm is 4% of 1 km.
Solution:
False
1 km = 1000 m = 1000 × 100 cm = 100000 cm
4% of 1km=(4100×100000)cm=4000cm

Question 71.
Out of 600 students of a school, 126 go for a picnic. The percentage of students that did not go for the picnic is 75.
Solution:
False
Total number of students = 600
Number of students went on a picnic = 126
∴ Number of students who did not go for the picnic = 600 – 126 = 474
Percentage of students who did not go for the picnic
=474600×100=79.16%

Question 84.
Express 1100 as a percent.
Solution:
1100=1%

Question 100.
45% of the population of a town are men and 40% are women. What is the percentage of children?
Solution:
Total percentage = 100
Percentage of men = 45
Percentage of women = 40
∴ Percentage of children = 100 – (45 + 40) = 100 – 85 = 15

 

Question 108.
A man travelled 60 km by car and 240 km by train. Find what percent of total journey did he travel by car and what percent by train?
Solution:
Distance travelled by car = 60 km
Distance travelled by train = 240 km
Total distance travelled = (60+240) km = 300 km
Percentage of journey travelled by car
=60300×100=20%
Percentage of journey travelled by train
=240300×100=80%

Question 111.
A person wanted to sell a scooter at a loss of 25%. But at the last moment he changed his mind and sold the scooter at a loss of 20%. If the difference in the two SP’s is ₹ 4000, then find the CP of the scooter.
Solution:
Let the C.P. of a scooter = ₹ x
S.P. of the scooter for a loss of 25%
=(100−25100)×x=34x
S.P. of the scooter for a loss of 20%
=(100−20100)×x=(80100)x=45x
Difference in both S.P.’s of the scooter
=45x−34x=120x
According to question,
120x=4000
⇒ x = 4000 × 20 = 80000

Question 115.
In an examination, there are three papers each of 100 marks. A candidate obtained 53 marks in the first and 75 marks in the second paper. How many marks must the candidate obtain in the third paper to get an overall of 70 percent marks?
Solution:
Total marks = 100 + 100 + 100 = 300
Marks obtained by the candidate in first paper = 53
Marks obtained by the candidate in second paper = 75
Let the marks obtained by the candidate in third paper = x
Total marks obtained by the candidate = 53 + 75 + x – 128 + x
According to question,
(128+x)300×100=70
⇒ 128 + x = 3x 70
⇒ x = 210 – 128 = 82
So, the candidate must obtain 82 marks in the third paper.

Question 120.
What’s the Error? A student said that the ratios 34 and 916 were proportional. What error did the student make?
Solution:
34=3×44×4=1216≠916
Therefore 34 and 916 are not proportional.

Question 123.
A piece of cloth 5 m long shrinks 10 percent on washing. How long will the cloth be after washing?
Solution:
Length of cloth = 5m
Shrinking percentage after washing = 10%
∴ Length of cloth, after washing
= 5 – 10% of 5
=5−10100×5=5−0.5=4.5m

Question 124.
Nancy obtained 426 marks out of 600 and the marks obtained by Rohit are 560 out of 800. Whose performance is better?
Solution:
Percentage of marks obtained by Nancy
=426600×100=71%
Percentage of marks obtained by Rohit
=560800×100=70%
So, Nancy’s performance is better.

Value of the second and third scholarships = ₹ (20000 + 15000) = ₹ 35000
Now, value of the first scholarship = ₹ (60000 – 35000) = ₹ 25000

Question 126.
Ambika got 99 per cent marks in Mathe matics, 76 per cent marks in Hindi, 61 percent in English, 84 per cent in Science, and 95% in Social Science. If each subject carries 100 marks, then find the percentage of marks obtained by Ambika in the aggregate of all the subjects.
Solution:
Total maximum marks = 5 × 100 = 500
Total marks obtained by Ambika in all subjects = 99 + 76 + 61 + 84 + 95 = 415
Percentage of marks obtained by Ambika
=415500×100=83%

Question 139.
Geography Application: Earth’s total land area is about 148428950 km². The land area of Asia is about 30 per cent of this total. What is the approximate land area of Asia to the nearest square km?
Solution:
Earth’s total land area = 148128950 km²
Land area of Asia = 30% of 148428950 km²
=30100×148428950=44528685km2

 

Also Read: NCERT Exemplar Solutions Class 7 Maths Solutions Chapter 11 Exponents & Powers