Ratio and Proportion- 2 - UPSC Free MCQ Practice Test with solutions

Practice Test: Ratio & Proportion- 2 - Question 1

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

Detailed Solution: Question 1

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

Practice Test: Ratio & Proportion- 2 - Question 2

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. 34,000

Detailed Solution: Question 2

Let the present salaries be:
Ravi = 2x
Sumit = 3x
After each gets a ₹4,000 raise, the new salaries are:
Ravi = 2x + 4,000
Sumit = 3x + 4,000
Those new salaries are in the ratio 40 : 57, so
(2x + 4,000) / (3x + 4,000) = 40 / 57
Cross-multiply to solve for x:
57·(2x + 4,000) = 40·(3x + 4,000)
114x + 228,000 = 120x + 160,000
228,000 – 160,000 = 120x – 114x
68,000 = 6x
x = 68,000 / 6 = 11,333.33
Sumit’s present salary = 3x = 3 × 11,333.33 = ₹34,000

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Practice Test: Ratio & Proportion- 2 - Question 3

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

Detailed Solution: Question 3

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

Practice Test: Ratio & Proportion- 2 - Question 4

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

Detailed Solution: Question 4

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.

Practice Test: Ratio & Proportion- 2 - Question 5

The fourth proportional to 5, 8, 15 is:

A.
18
B.
24
C.
19
D.
20

Detailed Solution: Question 5

Let the fourth proportional to 5, 8, 15 be x.

Then, 5 : 8 = 15 : x

⇒ 5x = (8 × 15)

x = (8 × 15) / 5 = 24.

Practice Test: Ratio & Proportion- 2 - Question 6

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

Detailed Solution: Question 6

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.

Practice Test: Ratio & Proportion- 2 - Question 7

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

Detailed Solution: Question 7

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.

Practice Test: Ratio & Proportion- 2 - Question 8

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

A.
1.12
B.
1.2
C.
1.25
D.
1.30

Detailed Solution: Question 8

To solve the proportion 0.75 : x :: 5 : 8, we set up the equation:

0.75 / x = 5 / 8

Cross-multiplying gives:

5x = 0.75 × 8

This simplifies to:

5x = 6

Leading to:

x = 6 / 5 = 1.20

Practice Test: Ratio & Proportion- 2 - Question 9

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

Detailed Solution: Question 9

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.

Practice Test: Ratio & Proportion- 2 - Question 10

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

Detailed Solution: Question 10

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- 2 - Free MCQ Practice Test with solutions, UPSC

MCQ Practice Test & Solutions: Practice Test: Ratio & Proportion- 2 (10 Questions)

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?

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?

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?

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

The fourth proportional to 5, 8, 15 is:

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?

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:

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

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:

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.

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