NCERT Grade 7-Comparing Quantities-Answers – MySchoolPage

# NCERT Solutions for Class 7 Maths

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1.    To find ratios, both quantities should be in same unit.

(a) ₹ 5 to 50 paise

⇒ 5 × 100 paise to 50 paise                            [∵ ₹ 1 = 100 paise]

⇒ 500 paise to 50 paise

Thus, the ratio is

(b) 15 kg to 210 g

⇒ 15 × 1000 g to 210 g                            [∵ 1 kg = 1000 g]

⇒ 15000 g to 210 g

Thus, the ratio is

(c) 9 m to 27 cm

⇒ 9 × 100 cm to 27 cm                             [∵ 1 m = 100 cm]

⇒ 900 cm to 27 cm

Thus, the ratio is

(d) 30 days to 36 hours

30 × 24 hours to 36 hours                             [∵ 1 day = 24 hours]

720 hours to 36 hours

Thus, the ratio is

2.    ∵ 6 students need = 3 computers

∵ 1 student needs  computers

∵ 24 students need  computers

Thus, 12 computers will be needed for 24 students.

3.    (i) People present per km²

In Rajasthan  people km²

In U.P.  people per km²

(ii) Rajasthan is less populated.

4.

5.

6.    (i) Coloured part

∴ Percent of coloured part

(ii) Coloured part

∴ Percent of coloured part

(iii) Coloured part

∴ Percent of coloured part

7.     (a) 15% of 250

(b) 1% of 1 hour = 1% of 60 minutes = 1% of (60 x 60) seconds

(c) 20% of ₹ 2500

(d) 75% of 1 kg = 75% of 1000 g

8.    Let the whole quantity be x in given question:

10.  Sol.

11.  Given: Percentage of females = 30%

Percentage of males = 40%

Total percentage of females and males = 30 + 40 = 70%

Percentage of children = Total percentage – Percentage of males and females

= 100% – 70%

= 30%

Hence, 30% are children.

12.  Total voters = 15,000

Percentage of voted candidates = 60%

Percentage of not voted candidates = 100 – 60 = 40%

Actual candidates, who did not vote

Hence, 6,000 candidates did not vote.

13.  Let Meera’s salary be ₹ x.

Now, 10% of salary = ₹ 400

10% of x = ₹ 400

Hence, Meera’s salary is ₹ 4,000.

14.  Number of matches played by cricket team = 20

Percentage of won matches = 25%

Total matches won by them

Hence, they won 5 matches.

15.  (a) Cost price of gardening shears = ₹ 250

Selling price of gardening shears = ₹ 325

Since, S.P. > C.P., Therefore here is profit.

∴ Profit = S.P, – C.P. = 325 – 250 = ₹ 75.

Now profit %

Therefore, Profit = ₹ 75 and profit% = 30%

(b) Cost price of refrigerator = ₹ 12,000

Selling price of refrigerator = ₹ 13,500

Since, S.P. > C.P.,  therefore here is profit.

Now profit %

Therefore, Profit = ₹ 1,500 and profit % = 12.5%

(c) Cost price of cupboard = ₹ 2,500

Selling price of cupboard = ₹ 3,000

Since, S.P. > C.P., therefore here is profit.

∴ Profit = S.P. – C.P. = 3000 – 2500 = ₹ 500

Now Profit %

Therefore, Profit = ₹ 500 and Profit % = 20%

(d) Cost price of skirt = ₹ 250

Selling price of skirt = ₹ 150

Since, C.P. > S.P. therefore here is loss.

∴ Loss = C.P. – S.P. = 250 – 150 = ₹ 100

Now loss %

Therefore, Profit = ₹ 100 and Profit % = 40%

16.  (a) 3 : 1

Total part = 3 + 1 = 4

Therefore, Fractional part

⇒ Percentage of parts

⇒ Percentage of parts = 75% : 25%

(b) 2 : 3 : 5

Total part = 2 + 3 + 5 = 10

Therefore, Fractional part

⇒ Percentage of parts

⇒ Percentage of parts = 20% : 30% : 50%

(c) 1 : 4

Total part = 1 + 4 = 5

Therefore, Fractional part

⇒ Percentage of parts

⇒ Percentage of parts = 20% : 80%

(d) 1 : 2 : 5

Total part = 1 + 2 + 5 = 8

Therefore, Fractional part

⇒ Percentage of parts

⇒ Percentage of parts = 12.5% : 25% : 62.5%

17.  The decreased population of a city from 25,000 to 24,500.

Population decreased = 25,000 – 24,500 = 500

Decreased Percentage

Hence, the percentage decreased is 2%.

18.  Increased in price of car from ₹ 3,50,000 to ₹ 3,70,000.

Amount change = ₹ 3,70,000 – ₹ 3,50,000 = ₹ 20,000.

Therefore,        Increased percentage

Hence, the percentage of price increased is

19.  The cost price of T.V. = ₹ 10,000

Profit percent = 20%

Now,    Profit = Profit% of C.P.

Selling price = C.P. + Profit

= 10,000 + 2,000 = ₹ 12,000

Hence, he gets ₹ 12,000 on selling his T.V.

20.  Selling price of washing machine = ₹ 13,500

Loss percent = 20%

Let the cost price of washing machine be ₹ x.

Since, Loss = Loss% of C.P.

Therefore,        S.P. = C.P. – Loss

Hence, the cost price of washing machine is ₹ 16,875.

21.  (i) Given ratio = 10 : 3 : 12

Total part = 10 + 3 + 12 = 25

Part of Carbon

Percentage of Carbon part in chalk

(ii) Quantity of Carbon in chalk stick = 3 g

Let the weight of chalk be x g.

Then, 12% of x = 3

Hence the weight of chalk stick is 25 g.

22.  The cost of a book = ₹ 275

Loss percent = 15%

Loss = Loss% of C.P. = 15% of ₹ 275

Therefore,           S.P. = C.P. – Loss

= 275 – 41.25 = ₹ 233.75

Hence, Amina sells a book for ₹ 233.75.

23.  (a) Here, Principal (P) = ₹ 1,200, Rate (R) = 12% p.a., Time (T) = 3 years

Simple Interest

Now, Amount = Principal + Simple Interest

= 1200 + 432

= ₹ 1,632

(b) Here, Principal (P) = ₹ 7,500, Rate (R) = 5% p.a., Time (T) = 3 years

Simple Interest

Now, Amount = Principal + Simple Interest

= 7,500 + 1,125

= ₹ 8,625

24.  Here, Principal (P) = Z 56,000, Simple Interest (S.I.) = ! 280, Time (T) = 2 years

Hence, the rate of interest on sum is 0.25%.

25.  Simple Interest = Z 45, Rate (R) = 9% p.a., Time (T) = 1 years

Hence, she borrowed ₹ 500.

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