Ratio & Proportion Test

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Ratio & Proportion Test - 2

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Weekly Quiz Competition

Question 1
2 / -0.83

The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?

A
8 : 9

B
17 : 18

C
21 : 22

D
Cannot be determined

Solution

Originally, let the number of boys and girls in the college be 7x and 8x respectively.
Their increased number is (120% of 7x) and (110% of 8x).
⇒(120/100 ×7x) and (110/100 ×8x)
⇒(42x/5) and (44x/5)
∴The required ratio = (42x/5) : (44x/5) = 21 : 22
Question 2
2 / -0.83

Salaries of Ravi and Sumit are in the ratio 2 : 3. If the 'salary of each 'one of them is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit 's present salary?

A
Rs. 17,000

B
Rs. 20,000

C
Rs. 25,500

D
Rs. 38,000

Solution

Ratio of salaries of Ravi and Sumit = 2 : 3.
Increased salary = 4000 each.
New ratio of Ravi and Sumit = 40 : 57.
Calculation:
Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.
Then, (2x + 4000)/(3x + 4000) = 40/57
⇒57(2x + 4000) = 40(3x + 4000)
⇒6x = 68000
⇒3x = 34000
∴Sumit 's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38000.
Question 3
2 / -0.83

The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?

A
3 : 3 : 10

B
10 : 11 : 20

C
23 : 33 : 60

D
Cannot be determined

Solution

Let A = 2k, B = 3k, and C = 5k.
A 's new salary = (115/100) of 2k = (115/100 ×2k) = (23k/10)
B 's new salary = (110/100) of 3k = (110/100 ×3k) = (33k/10)
C 's new salary = (120/100) of 5k = (120/100 ×5k) = 6k
∴New ratio = (23k/10) : (33k/10) : 6k = 23 : 33 : 60
Question 4
2 / -0.83

If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?

A
2 : 5

B
3 : 7

C
5 : 3

D
7 : 3

Solution

Let 40% of A = (2/3) B.
Then, (40A/100) = (2B/3).
⇒(2A/5) = (2B/3).
⇒A/B = ((2/3) ×(5/2)) = 5/3.
∴A : B = 5 : 3.
Question 5
2 / -0.83

The fourth proportional to 5, 8, 15 is:

A
18

B
24

C
19

D
20

Solution

Let the fourth proportional to 5, 8, 15 be x.
Then, 5 : 8 = 15 : x
⇒5x = (8 ×15)
x = (8 ×15) / 5 = 24.
Question 6
2 / -0.83

In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there?

A
50

B
100

C
150

D
200

Solution

Let the number of 25 p, 10 p, and 5 p coins be x, 2x, and 3x respectively.
Then, the sum of their values = Rs.
(25x/100 + 10 ×2x/100 + 5 ×3x/100) = 60x/100
∴60x/100 = 30
x = (30 ×100) / 60 = 50
Hence, the number of 5 p coins = (3 ×50) = 150.
Question 7
2 / -0.83

Two number are in the ratio 3 : 5. If 9 is subtracted from each number, the new numbers are in the ratio 12 : 23. The smaller number is:

A
27

B
33

C
49

D
55

Solution

Let the numbers be 3x and 5x.
Then, (3x - 9) / (5x - 9) = 12 / 23
⇒23(3x - 9) = 12(5x - 9)
⇒9x = 99
⇒x = 11
∴The smaller number = (3 ×11) = 33.
Question 8
2 / -0.83

If 0.75 : x :: 5 : 8, then x is equal to:

A
1.12

B
1.2

C
1.25

D
1.30

Solution

(x ×5) = (0.75 ×8) ⇒x = (6/5) = 1.20
Question 9
2 / -0.83

The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:

A
20

B
30

C
48

D
58

Solution

Let the three parts be A, B, C. Then,
A : B = 2 : 3 and B : C = 5 : 8 = (5 ×3/5) : (8 ×3/5) = 3 : 24/5
⇒A : B : C = 2 : 3 : 24/5 = 10 : 15 : 24
⇒B = (98 ×15/49) = 30.
Question 10
2 / -0.83

In a garrison of 3600 men, the provisions were sufficient for 20 days at the rate of 1.5 kg per man per day. If x more men joined, the provisions would be sufficient for 12 days at the rate of 2 kg per man per day. Find x.

A
600

B
800

C
900

D
720

Solution

Let x be the number of new men joined the garrison,
The total quantity of food is = 3600(20) (1.5) kg ----------1
Now the available food will be consumed by (3600 + x) men
(3600 + x) (12) (2) kg --------------2
1 = 2
Solving both the equations
3600(20) (1.5) = (3600 + x) (12) (2)
108000 = 86400 + 24x
21600 = 24x
X = 900
900 more men joined the garrison.

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Ratio & Proportion Test - 2

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Ratio & Proportion Test - 2

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Question 1

8 : 9

17 : 18

21 : 22

Cannot be determined

Solution

Question 2

Rs. 17,000

Rs. 20,000

Rs. 25,500

Rs. 38,000

Solution

Question 3

3 : 3 : 10

10 : 11 : 20

23 : 33 : 60

Cannot be determined

Solution

Question 4

2 : 5

3 : 7

5 : 3

7 : 3

Solution

Question 5

18

24

19

20

Solution

Question 6

50

100

150

200

Solution

Question 7

27

33

49

55

Solution

Question 8

1.12

1.2

1.25

1.30

Solution

Question 9

20

30

48

58

Solution

Question 10

600

800

900

720

Solution

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