## Comparing Quantities Class 8 Extra Questions Maths Chapter 8

**Extra Questions for Class 8 Maths Chapter 8 Comparing Quantities**

### Comparing Quantities Class 8 Extra Questions Very Short Answer Type

Question 1.

Express the following in decimal form:

(a) 12%

(b) 25%

Solution:

(a) 12% = \(\frac { 12 }{ 100 }\) = 0.12

(b) 25% = \(\frac { 25 }{ 100 }\) = 0.25

Question 2.

Evaluate the following:

(a) 20% of 400

(b) 12\(\frac { 1 }{ 2 }\)% of 625

Solution:

Question 3.

If 20% of x is 25, then find x.

Solution:

20% of x = 25

Hence x = 125

Question 4.

Express the following as a fraction

(a) 35%

(b) 64%

Solution:

Question 5.

Express the following into per cent

(а) 1\(\frac { 3 }{ 5 }\)

(b) 2 : 5

Solution:

Question 6.

There are 24% of boys in a school. If the number of girls is 456, find the total number of students in the school.

Solution:

Let the total number of students be 100.

Number of boys = 24% of 100 = \(\frac { 24 }{ 100 }\) × 100 = 24

Number of girls = 100 – 24 = 76

⇒ If number of girls is 76, then total number of students = 100

⇒ If Number of girls is 1, then total number of students = \(\frac { 100 }{ 76 }\)

If Number of girls is 456, then total number of students = \(\frac { 100\times 456 }{ 76 }\) = 600

Hence, the total number of students in the school = 600

Question 7.

The cost of 15 articles is equal to the selling price of 12 articles. Find the profit per cent.

Solution:

Let CP of 15 articles be ₹ 100

CP of 1 article = ₹ \(\frac { 100 }{ 15 }\)

SP of 12 articles = ₹ 100

SP fo 1 article = ₹ \(\frac { 100 }{ 12 }\)

SP > CP

Hence, profit = 25%

Question 8.

An article is marked at ₹ 940. If it is sold for ₹ 799, then find the discount per cent.

Solution:

MP = ₹ 940

SP = ₹ 799

Discount = MP – SP = 940 – 799 = ₹ 141

Hence, discount = 15%

Question 9.

A watch was bought for ₹ 2,700 including 8% VAT. Find its price before the VAT was added.

Solution:

Cost of watch including VAT = ₹ 2,700

Let the initial cost of the watch be ₹ 100

VAT = 8% of ₹ 100 = ₹ 8

Cost of watch including VAT = ₹ 100 + ₹ 8 = ₹ 108

If cost including VAT is ₹ 108, then its initial cost = ₹ 100

If cost including VAT is ₹ 1, then its initial cost = ₹ \(\frac { 100 }{ 108 }\)

If cost including VAT is ₹ 2,700, then its initial cost = ₹ \(\frac { 100 }{ 108 }\) × 2700 = ₹ 2500

Hence, the required cost = ₹ 2,500

Question 10.

Find the amount if ₹ 2,000 is invested for 2 years at 4% p.a. compounded annually.

Solution:

### Comparing Quantities Class 8 Extra Questions Short Answer Tpye

Question 11.

A number is increased by 20% and then it is decreased by 20%. Find the net increase or decrease per cent. (NCERT Exemplar)

Solution:

Let the number be 100

20% increase = \(\frac { 20 }{ 100 }\) × 100 = 20

Increased value = 100 + 20 = 120

Now it is decreased by 20%

Decreased value = 120 – \(\frac { 120 }{ 100 }\) × 20 = 120 – 24 = 96

Net decrease = 100 – 96 = 4

Decrease per cent = \(\frac { 4 }{ 100 }\) × 100 = 4%

Hence, the net decrease per cent = 4%

Question 12.

Two candidates Raman and Rajan contested an election. Raman gets 46% of the valid votes and is#defeated by 1600 votes. Find the total number of valid votes cast in the election.

Solution:

Let the total number of valid votes be 100

Number of votes got by Raman = 46% of 100 = \(\frac { 46 }{ 100 }\) × 100 = 46

Number of votes got by Rajan = 100 – 46 = 54

Difference between the votes = 54 – 46 = 8

8% of Valid votes = 1,600

⇒ \(\frac { 8 }{ 100 }\) × Valid votes = 1,600

⇒ Valid votes = \(\frac { 1600\times 100 }{ 8 }\) = 20,000

Hence, the total number of valid votes = 20,000

Question 13.

A man whose income is ₹ 57,600 a year spends ₹ 43,200 a year. What percentage of his income does he save?

Solution:

Annual income of a man = ₹ 57,600

Amount spent by him in the year = ₹ 43,200

Net amount saved by him = ₹ 57,600 – ₹ 43,200 = ₹ 14,400

Percentage of his annual saving Saving = \(\frac { Saving }{ Income }\) × 100

= \(\frac { 14400 }{ 57600 }\) × 100

= 25%

Hence, the saving percentage = 25%

Question 14.

A CD player was purchased for ₹ 3,200 and ₹ 560 were spent on its repairs. It was then sold at a gain of 12\(\frac { 1 }{ 2 }\) %. How much did the seller receive?

Solution:

Cost price of the CD player = ₹ 3,200

Amount spent on its repairing = ₹ 560

Net cost price = ₹ 3,200 + ₹ 560 = ₹ 3,760

Hence, the required amount = ₹ 4,230

Question 15.

A car is marked at ₹ 3,00,000. The dealer allows successive discounts of 6%, 4% and 2\(\frac { 1 }{ 2 }\) % on it. What is the net selling price of it?

Solution:

Marked price of the car = ₹ 3,00,000

Net selling price after the successive discounts

Hence, the net selling price = ₹ 2,63,952

Question 16.

Ramesh bought a shirt for ₹ 336, including 12% ST and a tie for ₹ 110 including 10% ST. Find the list price (without sales tax) of the shirt and the tie together.

Solution:

List price of the shirt = \(\frac { 110 }{ 112 }\) × 336 = ₹ 300

List price of the tie = \(\frac { 100 }{ 110 }\) × 110 = ₹ 100

List price of both together = ₹ 300 + ₹ 100 = ₹ 400

Question 17.

Find the amount of ₹ 6,250 at 8% pa compounded annually for 2 years. Also, find the compound interest.

Solution:

Question 18.

Find the compound interest on ₹ 31,250 at 12% pa for 12\(\frac { 1 }{ 2 }\) years.

Solution:

Question 19.

Vishakha offers a discount of 20% on all the items at her shop and still makes a profit of 12%. What is the cost price of an article marked at ₹ 280? (NCERT Exemplar)

Solution:

Marked Price = ₹ 280

Discount = 20% of ₹ 280

= \(\frac { 1 }{ 2 }\) × 280 = ₹ 56

So selling price = ₹ (280 – 56) = ₹ 224

Let the cost price be ₹ 100

Profit = 12% of ₹ 100 = ₹ 12

So selling price = ₹ (100 + 12) = ₹ 112

If the selling price is ₹ 112, cost price = ₹ 100

If the selling price is ₹ 224, cost price = ₹ (\(\frac { 100 }{ 112 }\) × 224) = ₹ 200

Question 20.

Find the compound interest on ₹ 48,000 for one year at 8% per annum when compounded half yearly. (NCERT Exemplar)

Solution:

Principal (P) = ₹ 48,000

Rate (R) = 8% p.a.

Time (n) = 1 year

Interest is compounded half yearly

Therefore Compound Interest = A – P = ₹ (519,16.80 – 48,000) = ₹ 3,916.80.