RBSE Class 8 Maths Important Questions Chapter 8 Comparing Quantities

Rajasthan Board RBSE Class 8 Maths Important Questions Chapter 8 Comparing Quantities Important Questions and Answers.

RBSE Class 8 Maths Chapter 8 Important Questions Comparing Quantities

Multiple Choice Questions:

Question 1.
A basket contains 15 apple and 5 oranges. What is the ratio of number of oranges to number of apples?
(a) 1 : 3
(b) 15 : 5 
(c) 3 : 1
(d) 5 : 20
Answer:
(a) 1 : 3

Question 2.
20% of 3400 is  
(a) 340
(b) 680 
(c) 20
(d) 2720
Answer:
(b) 680 

Question 3.
The market price of a jeans is ₹ 220. What will be the selling price of 20% discount is given?
(a) \(\frac{220 \times 20}{100}\)
(b) \(\frac{220 \times 120}{100}\)
(c) \(\frac{220 \times 80}{100}\)
(d) \(\frac{220 \times 10}{80}\)
Answer:
(c) \(\frac{220 \times 80}{100}\)

Question 4.
If is the principal amount, R is the interest rate per annum and n is the in years. What will be the formula to derive compound interest when interest is compounded annually?
(a) P + \(\left(1+\frac{\mathrm{R}}{100}\right)^{n}\)
(b) P × \(\left(1+\frac{\mathrm{R}}{100}\right)^{2 n}\)
(c) P × \(\left(1+\frac{\mathrm{R}}{100}\right)^{n}\)
(d) \(\frac{\mathrm{P} \times \mathrm{R} \times n}{100}\)
Answer:
(c) P × \(\left(1+\frac{\mathrm{R}}{100}\right)^{n}\)

Question 5.
Find compound interest on ₹ 20,000 at 8% per annum for 2 years, compounded annually?
(a) ₹ 3200
(b) ₹ 1728
(c) ₹ 1600
(d) ₹ 3328
Answer:
(d) ₹ 3328

Question 6.
If interest is. compounded quarterly, the time period becomes:
(a) double
(b) four times
(c) triple
(d) no change
Answer:
(b) four times

Question 7.
80% students are good in mathematics out of 25 students. How much students are not good, in mathematics ?
(a) 10
(b) 5
(c) 15
(d) 20 
Answer:
(b) 5

Question 8.
The basic pay of a person is ₹ 1,40,000. If his pay is increased by 10% then his new pay will be
(a) ₹ 1,50,000
(b) ₹ 1,40,010
(c) ₹ 1,54,000
(d) ₹ 1,40,100
Answer:
(c) ₹ 1,54,000

Question 9.
Reductions given on marked price is known as
(a) Profit
(b) Loss
(c) Selling price
(d) Discount
Answer:
(d) Discount

Question 10.
The correct option among the following is
(a) Discount = Marked price + Sale price
(b) Discount = Marked price - Sale price
(c) Discount = Marked price + Purchase price
(d) Discount = Marked price - Purchase price
Answer:
(b) Discount = Marked price - Sale price

Question 11.
10% of 170 is
(a) 17
(b) 1.7
(c) 7
(d) 1 
Answer:
(a) 17

Fill in the blanks:

Question 1.
___________ is a reduction given on market price.
Answer:
Discount

Question 2.
These days, the prices include the tax known as ___________
Answer:
Value Added Tax (VAT)

Question 3.
The interest calculated on the amount of the previous year is known as  ___________
Answer:
Compound interest

Question 4.
If interest is compounded ___________, the rate of interest becomes half.
Answer:
half yearly.

Very Short Answer Type Questions:

Question 1.
Express the ratio 1 : 4 in percentage.
Answer:
1:4 = \(\frac{1}{4}=\frac{1}{4} \times \frac{100}{100}=\frac{25}{100}\) = 25%

Question 2.
Find the 15% of ₹ 375.
Answer:
15% of f 375 = \((\frac{15}{100})\) × 375
= 56.25

Question 3.
Ramu purchased a geyser for ₹ 2200 which included 10% VAT tax. What was the price of the geyser excluding VAT tax?
Answer:
Price of the geyser excluding
VAT tax = \(\frac{100}{110}\) × 2200 = ₹ 2000

Question 4.
What is conversion period?
Answer:
The time period after which the interest is added each time to form a new principal is called the conversion period.

Question 5.
What are the effects on the time period and the rate of interest is compounded half yearly?
Answer:
If interest is compounded half yearly, then time period becomes double and interest rate becomes half.

Question 6.
What are the effects on the time period and the rate of interest is compounded quarterly?
Answer:
If interest is compounded quarterly, then the period becomes 4 times, and interest rate becomes one-fourth.

Question 7.
Find CI on ₹ 12,600 for 2 years at 10% per annum compounded annually.
Answer:
We have, A = P\(\left(1+\frac{\mathrm{R}}{100}\right)^{n}\)
Where, Principal (P) = ₹ 12,600
Rate (R) = 10
Number of years (n) = 2
Amount (A) = ₹ 12,600\(\left(1+\frac{10}{100}\right)^{2}\)
= ₹ 12,600\(\left(\frac{11}{10}\right)^{2}\)
= ₹ 12,600 × \(\frac{11}{10} \times \frac{11}{10}\)
= ₹ 15,246

CI = A - P
= ₹ 15,246 - ₹ 12,600 = ₹ 2646

Question 8.
A car was bought at ₹ 3,00,000. Its value depreciated at the rate of 6% per annum. Find its value after one year.
Answer:
Value of car after one year
= ₹ 3,00,000(1 - \(\frac{6}{100}\))
= ₹ 3,00,000 × \(\frac{94}{100}\)
= ₹ 2,82,000

Short Answer Type Questions:

Question 1.
The population of a place increased to 55,125 in 2013 at a rate of 5% per annum find the population in 2011 that place.
Answer:
Let P in the population of that place in 2011
therefore
Present population = P × \(\left(1+\frac{5}{100}\right)^{2}\)
or 55125 = P × \(\frac{105}{100} \times \frac{105}{100}\)
P = \(\frac{55125 \times 100 \times 100}{105 \times 105}\)
= \(\frac{55125 \times 20 \times 20}{21 \times 21}\)
= 50,000
therefore the population as that place in 2011 was 50,000

Question 2.
Mahendra lent out Rs. 40,000 for one year at 6% annual rate of interest and if the interest is compounded half yearly, then how much amount Mahendra will get after one year?
Answer:
As per question P = Rs. 40,000
R = 6% annual = 3% half yearly n = 1 year = 2

half yearly Mahendra will get after one year
= 40,000 × \(\left(1+\frac{3}{100}\right)^{2}\)
= 40 000 × \(\frac{103}{100} \times \frac{103}{100}\)
= 4 × 103 × 103 = 42436

Question 3.
Rehana bought an air cooler for ₹ 3300 including VAT (Value Added Tax) of 10%. Find the price of the air cooler before VAT was added.
Answer:
The price includes the VAT, i.e., the value added tax. Thus, a 10% VAT means if the price without VAT is ₹ 100 then price including VAT is ₹ 110. Now, when price including VAT is ₹ 110, original price is ₹ 100. Hence when price including tax is ₹ 3300, the original price = ₹ \(\frac{100}{110}\) × 3300 = ₹ 3000.

Question 4.
Shahid bought an article for ₹ 784 which included GST of 12%. What is the price of the article before GST was added ?
Answer:
Let original price of the article be ₹ 100. GST = 12%.
Price after GST is included = ₹ (100+12) = ₹ 112
When the selling price is ₹ 112 then original price = ₹ 100.
When the selling price is ₹ 784, then original price = ₹ \(\frac{100}{12}\) × 784 = ₹ 700