Comparing Quantities Test

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Comparing Quantities Test - 7

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Question 1
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An aluminium rod, 90 cm long, is bent to form a rectangle whose length and breadth are in respective ratio of 5 : 4. What is the area of the rectangle?

A
350 cm²

B
470 cm²

C
500 cm²

D
520 cm²

Solution

Let the length and breadth of the rectangle formed be 5x and 4x, respectively.
Perimeter of rectangle = Length of the rod
So, 2(4x + 5x) = 90
18x = 90

x = = 5

Length of the rectangle = 5 × 5 = 25 cm
Breadth of the rectangle = 4 × 5 = 20 cm
Area of rectangle = 25 x 20 = 500 cm²
Question 2
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Mohit bought a water dispenser that can hold 10 litres of water. What percentage of total capacity of the water dispenser is 600 cm³?

A
2%

B
6%

C
5%

D
8%

Solution

1 litre = 1000 cm³
10 litres = 10,000 cm³

Now, let the percentage be x.
Then,
x% of 10,000 = 600

× 10,000 = 600

100x = 600

x = 6
Therefore, 600 cm³ is 6 percent of 10 litres.
Hence, option 2 is correct.
Question 3
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If 120% of a number is 24000, then what is the number?

A
20000

B
21000

C
22000

D
23000

Solution

Let the number be x.

120% of x = 24000

(120/100) × x = 24000

x = = 20000
Question 4
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Which among the following is not equal to 4.5%?

A
45 out of 1000

B
9 out of 200

C
180 out of 400

D
27 out of 600

Solution

Let us consider all the options:

Option 1: × 100 = 4.5%

Option 2: × 100 = 4.5%

Option 3: × 100 = 45%

Option 4: × 100 = 4.5%

Since the value in option 3 is not 4.5, option 3 is correct.
Question 5
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Various steps involved in finding x : y, if=, are given as options. Which of the options represents the third step?

A
3 × (3x + 2y) = 4 × (2x + 4y)

B
9x - 8x = 16y - 6y

C
x = 10y

D
9x + 6y = 8x + 16y

Solution

Given,=

Step 1: 3 × (3x + 2y) = 4 × (2x + 4y)

Step 2: 9x + 6y = 8x + 16y

Step 3: 9x - 8x = 16y - 6y

Step 4: x = 10y

Hence, option 2 represents the third step.
Question 6
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The ratio of the length of ribbon P to that of ribbon Q is 2 : 3 and the ratio of the length of ribbon Q to that of ribbon R is 5 : 6. If the length of the longest of the three ribbons is 45 cm, then find the total length of all three ribbons.

A
105.5 cm

B
107.5 cm

C
110 cm

D
112.5 cm

Solution

Let the lengths of ribbon P and ribbon Q be 2x and 3x, respectively.

Given:

Length of ribbon R = x Length of ribbon Q

Length of ribbon R = × 3x =

Since ribbon R is the longest ribbon, x can be calculated as

= 45

x = = 12.5

Length of ribbon P = 2x = 2 × 12.5 = 25 cm
Length of ribbon Q = 3x = 3 × 12.5 = 37.5 cm
Length of ribbon R (longest) = 45 cm
Total length of all three ribbons = 25 + 37.5 + 45 = 107.5 cm
Question 7
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What value should come in place of the question mark (?) in the following equation?

24% of 1680 = 36% of ?

A
1120

B
1986

C
2220

D
2110

Solution

24% of 1680 = 36% of ?
Question 8
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If A exceeds B by 25%, then by what percent is B less than A?

A
25%

B
20%

C
15%

D
5%

Solution

Let B = 100

Now, 25% of 100 = = 25

Therefore, A = 100 + 25 = 125
Percent by which B is less than A =
= = 20%
Question 9
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What percent of 2 days is 1080 minutes?

A
37.50%

B
35%

C
30.50%

D
28%

Solution

2 days = 48 hours
1 hour = 60 minutes
2 days = 60 × 48 = 2880 minutes

Required % = × 100 = 37.50%
Question 10
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10 pencils are bought for Rs. 8 and 8 of them are sold for Rs. 10. Find the gain/loss percentage in this case.

A
56.25% loss

B
56.25% gain

C
65.25% loss

D
65.25% gain

Solution

C.P. of 10 pencils = Rs. 8

C.P. of 1 pencil = = Rs.

Also, S.P. of 8 pencils = Rs. 10

So, S.P. of 1 pencil = = Rs.

Now, profit = S.P. – C.P.

= - =

Profit % = x 100 = × 100
= 56.25%
Question 11
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What percentage of the following figure is shaded?

A
15%

B
25%

C
40%

D
75%

Solution

Total number of squares = 100

Number of shaded squares = 25

Required percentage = × 100 = 25%

Question 12

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Choose the INCORRECT match:

	Item	S.P. (in Rs.)	Profit/Loss	C.P. (in Rs.)
(A)	Bottle	250	25% profit	200
(B)	Book	150	50% profit	100
(C)	Table	200	40% loss	280
(D)	Toy Car	450	25% loss	600

(A)

(B)

(C)

(D)

Solution

(A)
C.P. of bottle = Rs. 200
S.P. of bottle = Rs. 250

Profit % = × 100

= = 25%

(B)
C.P. of book = Rs. 100
S.P. of book = Rs. 150

Profit % = × 100

= = 50%

(C)
C.P. of table = Rs. 280
S.P. of table = Rs. 200

Loss % = × 100

= = 28.57% (Incorrect)

(D)
C.P. of toy car = Rs. 600
S.P. of toy car = Rs. 450

Loss % = × 100

= = 25%

Question 13
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The simple interest on a certain sum of money (principal) is of that sum. Find the rate of interest and time, if both are numerically equal.

A
%; 7 years and 6 months

B
%; 6 years and 8 months

C
%; 8 years and 8 months

D
%; 3 years and 6 months

Solution

Let P be the principal amount.
Rate of interest = R
Time = T
Simple Interest = SI
Now,

SI =

Now, SI = P, so

P =

R × R =

R = = %

T = years or 7 years and 6 months
Question 14
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Express 82 m as a percentage of 2 km 50 m.

A
5%

B
4%

C
%

D
%

Solution

2 km 50 m = 2000 m + 50 m = 2050 m

Required percentage = × 100 = 4%
Question 15
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Two numbers are in the ratio of 3 : 2. When each number is increased by 14, the ratio becomes 5 : 4. The numbers are

A
21 and 14

B
24 and 16

C
12 and 8

D
3 and 6

Solution

Given Ratio = 3 : 2
Let the numbers be 3x and 2x.
According to question:
=
12x + 56 = 10x + 70
2x = 14
x = 7

Therefore, the numbers are:
3x = 3 × 7 = 21
2x = 2 × 7 = 14
Question 16
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In an election between two candidates, the candidate who received 40% of the votes loses by 14,000 votes. What is the total number of votes received by the winning candidate?

A
42,000

B
40,000

C
38,000

D
36,000

Solution

Let the total number of votes polled be x.

Then, 40% of x + 14,000 = 60% of x
+ 14,000 =
= 14,000

x == 70,000

Total number of votes polled = 70,000

Number of votes received by the winning candidate = 60% of 70,000

× 70,000 = 42,000
Question 17
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A contractor employed 400 men to build a bridge in 120 days. After 20 days, they were joined by 100 more men. In how many days was the remaining work completed?

A
55

B
60

C
70

D
80

Solution

Let the total work be 1.

Work done in 120 days by 400 men = 1

Work done in 1 day by 400 men =

Work done in 20 days by 400 men = × 20 =
Now, of work is left for (400 + 100) = 500 workers to complete.

Let the number of days taken by them to finish the remaining work be x.

500 × x =× 400 × 120

x = = 80 days
Question 18
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A man sold two jackets for Rs. 1500 each, neither losing nor gaining in the transaction. If he sold one jacket at a profit of 20%, then he sold the other jacket at a loss of

A
%

B
%

C
%

D
%

Solution

Selling price of 1 jacket = Rs. 1500

Profit % = 20%

C.P. = = = Rs. 1250

The man neither gains nor loses in the transaction.

Therefore, cost price of second jacket

= S.P. of 2 jackets - C.P. of 1 jacket

= (3000 - 1250) = Rs. 1750

Now, C.P. of second jacket = Rs. 1750

Selling Price = Rs. 1500

Loss % = =

= = %
Question 19
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By selling a bucket for Rs. 135, a man loses of his outlay. If it were sold for Rs. 182, what would be the gain percentage?

A
7.85%

B
8.15%

C
9.15%

D
9.55%

Solution

Selling price of the bucket = Rs. 135
Let the cost of the bucket be x.
Loss = C.P. - S.P.
Loss = = x - 135 or 135 =
x = Rs. 168.75
Cost price of bucket = Rs. 168.75
Now, profit = S.P. - C.P.
182 - 168.75 = 13.25

Profit % = × 100

= 7.85%
Question 20
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Ram purchased 100 pens for Rs. 500 and sold them for Rs. 550, while Raghav purchased 100 pens for Rs. 600 and sold them for Rs. 750. For whom is the profit percentage higher and by how much?

A
Raghav, 15 %

B
Ram, 15%

C
Raghav, 10%

D
Ram, 5%

Solution

Cost price of pens purchased by Ram = Rs. 500
S.P. = Rs. 550
Profit of Ram = S.P. - C.P. = 550 - 500 = Rs. 50
Profit % == 10%
Cost price of pens purchased by Raghav = Rs. 600
S.P. = Rs. 750
Profit = 750 - 600 = Rs. 150
Profit % == 25%
Raghav's profit percentage is higher by (25 - 10) = 15%.

Question 21

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Match the following:

Column I	Column II
i. Atul sells his bike for Rs. 25,000 at a profit of 25%. The cost price of the bike was	P. 12
ii. Ram deposits a certain sum of money in bank at the rate of 4% for 4 years, and the interest earned is Rs. 420. Find the amount deposited by Ram.	Q. 2625
iii. The ratio of boys to girls in a classroom is 4 : 9, and the number of girls is 27. How many boys are there in the class?	R. 20000

i - Q, ii - P, iii - R

i - R, ii - P, iii - Q

i - R, ii - Q, iii - P

i - Q, ii - R, iii - P

Solution

i. SP = Rs. 25,000
Profit % = 25%

Profit % =

25% =

25CP = 25,00,000 - 100CP
125CP = 25,00,000
CP = Rs. 20,000

ii. SI = Rs. 420
R = 4%
T = 4 years

= SI

P = = Rs. 2625

iii. Boys : Girls = 4 : 9
Let the numbers of boys and girls be 4x and 9x, respectively.
Now, 9x = 27.
x = 3
Boys = 4x = 4 x 3 = 12

Question 22
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Determine whether the given statements are true (T) or false (F) and choose the correct option:

I. Raghav had Rs. 12,000. He spent 25% of it on shopping and gave the rest to her mom. The amount that he gave to her mom was Rs. 8000.
II. Sonia went to a shop and bought 56 lipsticks, 34 eyeliners and 72 combs. The shopkeeper had 100 units of each of these items. She bought 54% of the total units of all three items.
III. Karan bought some apples for Rs. 200 and sold them for Rs. 250. His profit percentage was 25%.

A

B

C

D

Solution

I. Raghav had Rs. 12,000.
He spent 25% on shopping.
Money left after shopping = 12,000 - (12,000 x 0.25) = Rs. 9000 (False)

II. Number of lipsticks bought = 56
Number of eyeliners bought = 34
Number of combs bought = 72
Total units bought = 56 + 34 + 72 = 162
Total number of available units = 300

Percentage = x 100 = 54% (True)

III. C.P. = Rs. 200
S.P. = Rs. 250

Profit = x 100 = 25% (True)
Question 23
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Which of the following statements is/are correct?

I. A sum of money is to be distributed among A, B and C in the respective ratio of 5 : 2 : 4. If C gets Rs. 1000. then B will get Rs. 550.
II. There are 15 persons invited for an interview. Out of them, 3 decline the invitation. The percentage of persons who accept the invitation is 80%.

A
Only statement 1

B
Only statement 2

C
Both statements 1 and 2

D
Neither statement 1 nor statement 2

Solution

1. Let A, B and C get 5x, 2x and 4x, respectively.
C gets Rs. 1000.
So, 4x = 1000
x = Rs. 250
Therefore, B gets 2x = Rs. 250 x 2 = Rs 500 (False)

2. Number of persons invited = 15
Number of persons who decline = 3
So, remaining persons = 15 - 3 = 12
Percentage of remaining persons = x 100 = 80% (True)
Question 24
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Directions: In this problem, a question is asked followed by three statements, numbered (i), (ii) and (iii). Read all the statements carefully and decide which of them is/are required to answer the question.

What is the principal?

(i) Total simple interest on the sum is Rs. 100.
(ii) Total simple interest on the sum is Rs. 500 for 5 years.
(iii) The rate of interest is 5% per annum.

A
Both (i) and (ii)

B
Both (ii) and (iii)

C
All of them

D
Any two of the three

Solution

Both ii and iii are required.
Given: SI = Rs. 500
R = 5%
T = 5 years

SI =
P = Rs. 2000
Question 25
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Fill in the blanks:

(i) If Ankita travels 220 km in 20 hours, then she will travel ______ km in 40 hours at the same speed.
(ii) If the cost price of a mobile is Rs. 12,000 and the selling price is Rs. 14,000, then the amount of profit will be ______.
(iii) If the ratio of the number of males to that of females is 3 : 7 and the number of males is 21, then the number of females is _____.

A
(i) - 400, (ii) - Rs. 3000, (iii) - 49

B
(i) - 440, (ii) - Rs. 2000, (iii) - 49

C
(i) - 440, (ii) - Rs. 2000, (iii) - 50

D
(i) - 440, (ii) - Rs. 3000, (iii) - 21

Solution

(i) Since speed remains the same, distance is directly proportional to time.

d₂ = 440 km

(ii) C.P. = Rs. 12,000
S.P. = Rs. 14,000
Profit = 14,000 - 12,000 = Rs. 2000

(iii) Let the numbers of males and females be 3x and 7x, respectively.
Number of males = 21
So, 3x = 21
x = 7
Number of females = 7x = 7 x 7 = 49