# Free Comparing Quantities 02 Practice Test - 8th Grade

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

A.

₹ 2,25,000

B.

₹ 2,17,500

C.

₹ 2,40,000

D.

₹ 2,23,000

#### SOLUTION

Solution : B

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

A=P×[1r100]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₹ 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 =2,25,0007,500 =  2,17,500

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

A.

6,620

B.

6,000

C.

26,620

D.

₹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 - P

Here, P =  20,000, r = 10 %, and n = 3 years

A=20,000×[1+10100]3
A=20,000×[11×11×1110×10×10]
A =
₹  26,620

So, C.I = 26,620 - 20,000 = ₹ 6,620

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.

A.

20%

B.

25%

C.

30%

D.

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           = 20000

Percentage of loss=losscost price×100

=2000080000×100=25%

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

A.

42,20,000

B.

46,20,000

C.

44,20,000

D.

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

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.

A.

True

B.

False

#### SOLUTION

Solution : A

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

So, fraction of apples =1030=13

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?

A.

2000

B.

1500

C.

1000

D.

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

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.

A.

Loss of 300

B.

Profit of 300

C.

Profit of 600

D.

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  ₹ (12,30012,000) = ₹ 300.

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.

A.

5421

B.

4830

C.

8545

D.

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

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?

A.

₹ 3120

B.

3300

C.

₹ 3395

D.

₹ 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
= ₹ 120

Final bill amount = 3000 + ₹ 120 = ₹ 3120

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.

A.

4000

B.

2000

C.

1000

D.

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.