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×[110100]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.