# Free Comparing Quantities 03 Practice Test - 7th grade

Ashin invested an amount of Rs. 13,900 divided into two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B (in rupees)?

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#### SOLUTION

Solution :

Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900 - x).

Then

14×x×2100   +    (13900x)×11×2100 = 3508

28x+13900×2222x100= 3508

28x+13900×2222x=3508×100

28x - 22x = 350800 - (13900 × 22)

6x = 45000

x = 7500

So, sum invested in Scheme B = Rs. (13900 - 7500) = Rs. 6400

The cost price of 20 articles is the same as the selling price of articles.The value of x is (given profit =20%).

#### SOLUTION

Solution :

Let C.P. of each article be Rs. 1

=> C.P. of x articles = Rs.x.

S.P. of x articles = Rs. 20.

Profit = Rs. (20 - x).

20xx×100 = 25.

2000 - 100x = 25x.

125x = 2000.

x = 16.

The table below shows the number of children with different heights.Height110cm120cm130cm140cmNo of children22252132

What is the percentage of students whose height is more than 125 cm?

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#### SOLUTION

Solution :

Number of students whose height is more than 125cm = 21 + 32 = 53

Total number of students = 22 + 25 + 21 + 32 = 100

Percentage of students whose height is more than 125cm = 53100 × 100 = 53%

Ram can type 50 words per minute. If the ratio of words typed by Rahul and Ram is 1 : 2, then Rahul can type _______ words per minute.

#### SOLUTION

Solution :

Given the ratio of words typed by Rahul to Ram = 1:2

Let the number of words that Rahul can type be x

∴  12  =  Number of words typed by RahulNumber of words typed by Ram

12 =  Number of words typed by Rahul50

The number of words typed by Rahul = 12 × Number of words typed by Ram

= 12 × 50 = 25

Rahul can type 25 words per minute.

A fruit seller sold 40% of his apples and was left with 420 apples. What is the number of apples he had initially?​

A.

708

B.

600

C.

700

D.

605

#### SOLUTION

Solution : C

Let the number of apples he had initially be x.

Given, (100 - 40)% of x = 420

60% of x = 420

60100×x=420

0.6x = 420

Hence,

x=4200.6 = 42006 = 700

Therefore, the number of apples he had initially = 700

Shubendhu buys an old scooter for 4700 and spends 800 on its repairs. If he sells the scooter for 5800, what is his gain (in percentage)?

A.

6512%

B.

7711%

C.

6011%

D.

7712%

#### SOLUTION

Solution : C

Cost Price (C.P.) =  ₹ (4700+800) =  ₹ 5500.

Selling Price (S.P.) = ₹ 5800.

Gain = (S.P.)-(C.P.)= ₹ (5800 - 5500) = ₹ 300

Gain%  = GainC.P×100%

= 3005500×100%

=6011%

Ram drew a line segment of length 10 cm. He told Arjun that he has scaled down. The scale used by him is 2cm = 100m. What is the actual length of the line segment?

A.

50m

B.

500m

C.

600m

D.

1000m

#### SOLUTION

Solution : B

Since 2cm is equivalent to 100m,

1 cm is equivalent to 1002 = 50m.

Therefore, actual length of the line = 10 × 50 = 500m.

1525 is equivalent to ____.

A.

5

B.

15

C.

35

D.

53

#### SOLUTION

Solution : C

1525 = 35.   [By dividing both numerator and denominator by 5]

Find the ratio of 5 km to 500 m.

A.

1 : 100

B.

10 : 1

C.

100 : 1

D.

1 : 1000

#### SOLUTION

Solution : B

Since,
1 km = 1000 m and 5 km = 5000 m

Then, required ratio
=5000500 = 10 : 1

After recording the height and weight, Ted wanted to know who is taller? Him or Ned. For that, he asked Ned’s height. He told that it was 135 cm and Ted’s height was 4.5 ft. Given 1 foot = 0.3 meters, what will be the value of Neds heightTeds height?

A.

100

B.

30

C. 1
D. 0.01

#### SOLUTION

Solution : C

To compare two similar quantities, their units must be same. Ned’s height is in cm and Ted’s height is in ft. In order to compare those heights, we need to convert both the heights to same units.

Thus, 4.5 ft=4.5×0.3 m=1.35 m
Now, 1m = 100 cm
Thus, 4.5 ft=1.35 m=1.35×100 cm=135 cm
Thus, Neds heightTeds height=135135=1