# Free Comparing Quantities 03 Practice Test - 8th Grade

### Question 1

For a compound interested sum which of the following details are necessary?

Principal

Interest rate

Time taken to return loan

Conversion periods

#### SOLUTION

Solution :A, B, and D

For a sum whose interest is calculated by compounding, the following things need to be defined:

-Principal

-Rate of interest

-Conversion periods (annual, half-yearly)

The time taken to return the loan is not fixed. Based on the time taken and the other fixed details above, the final interest is calculated.

### Question 2

Ramesh invests ₹ 12800 for three years at the rate of 10% per annum compounded annually. Find the sum Ramesh receives at the end of the first year.

₹15060

₹14000

₹14080

₹13090

#### SOLUTION

Solution :C

Principal = ₹ 12800, Rate =10%

Interest for one year =P × r × t100=(12800 × 10 × 1)100=₹ 1280

So, sum due after one year =12800+1280=₹14080

### Question 3

The list price of a frock is Rs 220. A discount of 20% is announced on sales. The sale price in Rs. is

#### SOLUTION

Solution :Marked price is same as the list price.

20% discount means that on Rs 100 (MP), the discount is Rs 20.

By unitary method, on Re 1 the discount will be Rs 20100

On Rs 220, discount = Rs 20100 x 220 = Rs 44

The sale price = (Rs 220 - Rs 44) or Rs 176

OR

A discount of 20% means for MP of Rs 100, the discount is Rs 20.

Hence, the sale price is Rs 80.

Using unitary method, when MP is Rs 100, sale price is Rs 80;

When MP is Re 1, sale price is Rs 80100

Hence, when MP is Rs 220, sale price = Rs 80100 x 220 = Rs 176.

### Question 4

The prices of all the televisions in a shop are to be increased by 8%. Calculate the new price of a television that originally costs Rs.150.

Rs. 162

#### SOLUTION

Solution :A

8% of 150=8100×150=Rs. 12

New price =150+12=Rs. 162

### Question 5

What must be added to each term of the ratio 2 : 3, so that it becomes equal to 4 : 5?

3

2

9

4

#### SOLUTION

Solution :B

Let the number to be added be x, then (2+x):(3+x)=4:5

⇒2+x3+x=45⇒5(2+x)=4(3+x)⇒10+5x=12+4x⇒5x−4x=12−10⇒x=2

### Question 6

In a class, 60% of the students are girls and there are 20 boys. What is the strength of the class?

35

30

40

50

#### SOLUTION

Solution :D

Let the strength of the class be x.

Given that 60% are girls, so 40% are boys.

Now, 40%×x=20

(Since number of boys in the class is 20)

⇒40100×x=20

⇒x=20×10040

⇒x=50

Therefore, total number of students in the class is 50.

### Question 7

I had some money with me. I bought a heavy painting for some price, transported it to my house and sold it for some price. If I am calculating profit made, what will be the effective cost price?

Cost price of the painting

Amount spent for its transportation

Cost price of the painting + Amount spent for its transportation

Cost price of the painting + 12 (Amount spent for its transportation)

#### SOLUTION

Solution :C

Here, amount spent for its transportation is the overhead charge (amount spent for repairs/transportation/labour charges) which should always be added to the cost price of the item while calculating profit made on the sale.

Therefore, effective cost price is the sum of cost price of the painting and amount spent for its transportation.

### Question 8

The difference between compound interest and simple interest on an amount of ₹15,000 for 2 years is ₹96. What is the rate of interest per annum?

10%

9%

8%

12%

#### SOLUTION

Solution :C

Given that, principal, P=₹15000 and time period, n=2 years .

Let the rate of interest per annum be r.

Simple interest in 2 years

S.I=15000×r×2100

⇒S.I=300r

Compound interest C.I=A−P=15000(1+r100)2−15000, here, A is the amount.

Given that C.I−S.I=96

(Since C.I > S.I)

⇒15000(1+r100)2−15000−300r=96

⇒15000(1+r100)2−300r=15096

⇒15000(1+r210000+2r100)−300r=15096

⇒15000+15r210+300r−300r=15096

⇒15r210=96

⇒15r2=960

⇒r2=64

⇒r=±8

∵ Rate of interest cannot be negative, so r=8%

### Question 9

A shopkeeper buys an article at a discount of 30% on the printed price. He spends ₹40 on transportation of the article. After charging goods and service tax at the rate of 7% on the printed price, he sells the article for ₹ 856. Find his profit percentage.

3312%

3513%

3918%

3313%

#### SOLUTION

Solution :D

Let the printed price of the article be x.

GST=7% of x=(7100)×x= 7x100

Selling price=x+7x100= 107x100

As per question, 107x100=₹ 856

⇒x=856×100107=₹ 800

Hence, printed price =₹ 800

Discount = 30% of ₹ 800 =(30100)×800=₹ 240

Cost price of the article=800−240=₹ 560

Overhead=cost of transportation =₹ 40

Actual cost price=560+40=₹ 600

GST is charged by the government on the sale of an item. It is collected by the shopkeeper from the customer and given to the government. Hence, while calculating profit we will not include GST amount.Profit=Printed price−Actual cost price =800−600=₹200.

Profit %=(profitcost price)×100 =(200600)×100

=1003% =3313%

### Question 10

The cost of a bike, purchased 2 years ago, depreciates at the rate of 20% every year. If its present worth is **₹ **35600, find its purchase price.

₹ 55625

₹ 43175

₹ 49352

₹ 50625

#### SOLUTION

Solution :A

Let the present value of the car be V which is

₹35600,

Time, n=2 years, and rate of interest, r=20%Let the purchase price be V0

Using, V=V0(1−r100)n

⇒35600=V0(1−20100)2⇒35600=V0(80100)2=V0(1625)⇒V0=35600×2516=₹ 55625