# Free Comparing Quantities 02 Practice Test - 8th Grade

### Question 1

The cost of Maruti 800 in the year 1998 was ₹ 2,50,000. After the end of one year and four months, the price underwent depreciation by 10% per annum. Its new price is

₹ 2,25,000

₹ 2,17,500

₹ 2,40,000

₹ 2,23,000

#### SOLUTION

Solution :B

Depreciation means a decrease in the value due to use and age of the item.

A=P×[1−r100]n, where A is the amount, P is the principal, r is the rate of interest and n is the time period.

So, price at the end of one year =2,50,000×[1−10100]1= ₹ 2,25,000

Depreciation for next four months =2,25,000×10×1100×3 = ₹ 7500

So, the depreciated value after one year and four months =2,25,000−7,500 = ₹ 2,17,500

### Question 2

Find the compound interest on ₹ 20,000 for 3 years at 10% per annum compounded annually.

₹ 6,620

₹6,000

₹ 26,620

₹26,000

#### SOLUTION

Solution :A

A=P×[1+r100]n, where P is the principal, r is the rate of interest and n is the time period.

C.I = A - PHere, P = ₹ 20,000, r = 10 %, and n = 3 years

A=20,000×[1+10100]3

A=20,000×[11×11×1110×10×10]

A = ₹ 26,620So, C.I = 26,620 - 20,000 = ₹ 6,620

### Question 3

A motorbike was sold by a showroom for ₹ 80,000. The owner then sold this bike at ₹ 60,000. Find the percentage of profit or loss.

20%

25%

30%

35%

#### SOLUTION

Solution :B

As the selling price is less than the cost price, the owner incurred loss.

Loss = Difference in the amount for which it was purchased and the amount for which it was sold.

∴Loss=₹ 80000−₹ 60000 =₹ 20000Percentage of loss=losscost price×100

=2000080000×100=25%

### Question 4

The accommodation in an apartment costs ₹ 42 lakh. After 6 months, there was a 10% price hike, the new cost is:

42,20,000

46,20,000

44,20,000

44,60,000

#### SOLUTION

Solution :B

The price hike is 10%. So, 10% of 42,00,000 would give you the price hike.Hence, 10100×42,00,000=4,20,000

So, adding this amount to the previous price i.e. 42 lakhs would give you the new price.

So, 42,00,000 + 4,20,000 = ₹ 46,20,000

### Question 5

In a bag, there is a total of 30 fruits. Out of which, 20 are oranges and 10 are apples.The fraction of apples in the bag is 13.

True

False

#### SOLUTION

Solution :A

Fraction of apples =Number of applesTotal number of fruits in the bag

So, fraction of apples =1030=13

### Question 6

According to a survey conducted in a city, 25% were doctors, 30% engineers, 15% businessmen and rest were illiterates. What is the number of illiterates if the total population of the city is 5000?

2000

1500

1000

500

#### SOLUTION

Solution :B

Given: Out of total population, 25% were doctors, 30% engineers, 15% businessmen and rest were illiterates.

Hence, percentage of illiterates =100−(25+30+15)=30%So, number of illiterates =30% of 5000

=30100×5000

=1500

### Question 7

A shopkeeper sold two bats which have a cost price of ₹6000 each. He makes a profit of 10% on one bat but a loss of 5% on the other bat. Find the overall profit or loss in the entire transaction.

Loss of ₹300

Profit of ₹300

Profit of ₹600

Loss of ₹600

#### SOLUTION

Solution :B

Profit on one of the bats = 10% of ₹ 6000

= 10100×6000= ₹600

Hence, the Selling price

= Cost price + Profit

= ₹ (6000 + 600) = ₹ 6600

Loss on the other bat

= 5% of ₹ 6000

= 5100×₹ 6000

= ₹ 300

Selling price = Cost price - Loss

= ₹ (6000 - 300)

= ₹ 5700

Total cost price (CP) = ₹ 12000

Total selling price (SP) =₹6600+₹5700 = ₹ 12,300

Hence, as SP > CP, he has made a profit of ₹ (12,300−12,000) = ₹ 300.

### Question 8

Find the compound interest paid when a sum of ₹64,000 is invested for one year and six months at 5% per annum compounded half yearly.

₹5421

₹4830

₹8545

₹4921

#### SOLUTION

Solution :D

Given that P = ₹ 64,000 r = 5 % and n = 112 years

Since, the rate of interest is calculated annually , for 6 months it will be 2.5 %

A=P(1+r100)n

Here r = 52 % and n = 3 half years

A=64,000(1+52×100)3

A=64,000(4140)3

A=68921

∵ Compound interest = Amount - Principal

= 68921 - 64000

= ₹ 4921

### Question 9

A family went to a restaurant for dinner. The bill of ₹3000 was handed which was not inclusive of the 4% Goods and Service Tax (GST). The final bill amount would be?

₹ 3120

₹ 3300

₹ 3395

₹ 3595

#### SOLUTION

Solution :A

GST is calculated on the selling price. Since the bill amount is the selling price, the GST is added to the bill amount itself.

So, GST = 4% of ₹ 3000

= 4100×3000

= ₹ 120Final bill amount = ₹3000 + ₹ 120 = ₹ 3120

### Question 10

Shalini deposited ₹4,00,000 in a bank where she was promised an interest of 10%. She deposited it for a period of two years. Find the difference in the amount if the interest is calculated in a compounded manner to the amount interested in a simple manner.

₹4000

₹2000

₹1000

₹500

#### SOLUTION

Solution :A

When a principal is promised with an interest to be compounded annually, the amount after one year becomes the principal for the next year. So, 10100×400000=40,000

₹40,000 added to ₹4,00000 would be the new principal for the next year i.e. 4,40,000. The interest for the second year is calculated on the new principal amount: 10100×440000×1=44,000

So, the final amount after 2 years(compounded annually with 10% interest) = ₹440000 + 44000 = ₹4,84,000.If the principal would have been deposited for an annual simple interest for 10% for a period of two years would be 10100×400000×2=80,000

Therefore amount = ₹4,00000 + ₹80,000 = ₹4,80,000.So, compound interest is ₹4,000 more than a simple interest for a period of two years.