MCQ: Ratio and Proportion - 1 - SSC CGL MCQ

# MCQ: Ratio and Proportion - 1 - SSC CGL MCQ

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## 15 Questions MCQ Test Quantitative Aptitude for SSC CGL - MCQ: Ratio and Proportion - 1

MCQ: Ratio and Proportion - 1 for SSC CGL 2024 is part of Quantitative Aptitude for SSC CGL preparation. The MCQ: Ratio and Proportion - 1 questions and answers have been prepared according to the SSC CGL exam syllabus.The MCQ: Ratio and Proportion - 1 MCQs are made for SSC CGL 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for MCQ: Ratio and Proportion - 1 below.
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MCQ: Ratio and Proportion - 1 - Question 1

### If x : y = 3 : 1, what is the value of “x2 – y2 : x2 + y2”?

Detailed Solution for MCQ: Ratio and Proportion - 1 - Question 1

x2 – y2 : x2 + y2 = “3 × 3 – 1 × 1” : “3 × 3 + 1 × 1” = 4 : 5
Hence, Option D is correct.

MCQ: Ratio and Proportion - 1 - Question 2

### In a college, the ratio of the number of boys to the number of girls is 5 : 3. If 80 boys leave the college and 40 girls join the college, the number of the girls will become the same as the number of boys. What is the initial number of boys in the college?

Detailed Solution for MCQ: Ratio and Proportion - 1 - Question 2

Let the initial number boys = 5x
The initial number of girls = 3x
(5x – 80) = (3x + 40)
2x = 120
x = 60
Hence, Option C is correct.

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MCQ: Ratio and Proportion - 1 - Question 3

### The ratio of two numbers is 5 : 8 and their difference is 117. What is the smaller number among the two?

Detailed Solution for MCQ: Ratio and Proportion - 1 - Question 3

Hence, Option A is correct.

MCQ: Ratio and Proportion - 1 - Question 4

If the square of the sum of two numbers is equal to 4 times their product, what is the ratio of these numbers?

Detailed Solution for MCQ: Ratio and Proportion - 1 - Question 4

Let two numbers = x and y
(x + y)2 = 4 × x × y
x2 + y2 + 2xy = 4xy
x2 + y2 – 2xy = 0
(x – y) = 0
x = y
x : y = 1 : 1
Hence, Option A is correct.

MCQ: Ratio and Proportion - 1 - Question 5

In 450 litres mixture of acid and water, the ratio of acid and water is 7 : 5. What amount of water should be added to the mixture so that the ratio of acid to water becomes 3 : 5?

Detailed Solution for MCQ: Ratio and Proportion - 1 - Question 5

Let the quantity of mixed water:

700 = 450 + X
X = 250 liters
Hence, Option B is correct.

MCQ: Ratio and Proportion - 1 - Question 6

If m : n = 5 : 2, what is the value of (2m + 5n) : (3m – 5n)?

Detailed Solution for MCQ: Ratio and Proportion - 1 - Question 6

(2m + 5n) : (3m – 5n) = (2 × 5 + 5 × 2) : (3 × 5 – 5 × 2) = 20 : 5 = 4 : 1
Hence, Option A is correct.

MCQ: Ratio and Proportion - 1 - Question 7

A class has two sections, the average marks of all the students in the class is 80. The average marks of all the students of Section A is 75 and the average marks of all the students of Section B is 90. What is the ratio of the number of students in Section A to that in section B?

Detailed Solution for MCQ: Ratio and Proportion - 1 - Question 7

Let the number of students in Section A = A
The number of students in Section B = B
75A + 90B = 80 × (A + B)
10B = 5A
A : B = 2 : 1
Hence, Option C is correct.

MCQ: Ratio and Proportion - 1 - Question 8

A and B together have Rs. 19,350. If 5/9 of A’s amount is equal to 2/5 of B’s amount. What amount does A have?

Detailed Solution for MCQ: Ratio and Proportion - 1 - Question 8

Let's denote:

• A's amount as 'A'
• B's amount as 'B'

We are given two pieces of information:

1. A + B = 19350
2. (5/9)A = (2/5)B

Let's solve the equations:

From equation 2, we can find a relationship between A and B:

• (5/9)A = (2/5)B
• Multiplying both sides by 9/5:
• A = (18/25)B

Now, substitute A in equation 1 with (18/25)B:

• (18/25)B + B = 19350
• Combining like terms:
• (43/25)B = 19350
• Multiplying both sides by 25/43:
• B = 19350 * (25/43)
• B = 11250

Now we know B's amount. To find A's amount, substitute B in the equation A = (18/25)B:

• A = (18/25) * 11250
• A = 8100

So, A has Rs. 8100.

MCQ: Ratio and Proportion - 1 - Question 9

The sum of two numbers is equal to four times their difference. What is the ratio of the bigger number to the smaller number?

Detailed Solution for MCQ: Ratio and Proportion - 1 - Question 9

Let the number = x and y
x + y = 4 × (x – y)
x + y = 4x – 4y
5y = 3x
x : y = 5 : 3
Hence, Option C is correct.

MCQ: Ratio and Proportion - 1 - Question 10

A school has 900 students out of which 60% are boys. What is the ratio of 75% of total girls to 80% of total boys?

Detailed Solution for MCQ: Ratio and Proportion - 1 - Question 10

Boys = 60%
Girls = 100% – 60% = 40%
So the answer = 75% of 40% : 80% of 60% = 5 : 8
Hence, Option E is correct.

MCQ: Ratio and Proportion - 1 - Question 11

If a : b = 5 : 9 and b : c = 5 : 3, what is a : c?

Detailed Solution for MCQ: Ratio and Proportion - 1 - Question 11

Reqd. ratio → a : b = 5 × 5 : 9 × 3 = 25 : 27
Hence, Option B is correct.

MCQ: Ratio and Proportion - 1 - Question 12

If a : b : c = 4 : 5 : 2 and 2a – b + 3c = 54, what is the value of b?

Detailed Solution for MCQ: Ratio and Proportion - 1 - Question 12

Let a = 4x
b = 5x
c = 2x
2 × 4x – 5x + 3 × 2x = 54
9x = 54
x = 6
b = 5x = 5 × 6 = 30
Hence, Option E is correct.

MCQ: Ratio and Proportion - 1 - Question 13

In a regiment, the ratio of the number of gazetted officers to that of non-gazetted officers was 1 : 10. 10 gazetted officers joined the regiment and 10 non-gazetted officers left the regiment, so the ratio of the number of gazetted officers to that of non-gazetted officers became 1 : 8. What was the initial number of gazetted officers?

Detailed Solution for MCQ: Ratio and Proportion - 1 - Question 13

Let the initial number of gazetted officers = x
The initial number of non-gazetted officers = 10x

8x + 80 = 10x – 10
x = 45
Hence, Option D is correct.

MCQ: Ratio and Proportion - 1 - Question 14

Two numbers are in the ratio 5 : 7. On subtracting 20 from each, the new ratio becomes 7 : 10. What is the difference between the original numbers?

Detailed Solution for MCQ: Ratio and Proportion - 1 - Question 14

Let the numbers = 5x and 7x

50x – 200 = 49x – 140
x = 60
So the answer = 7x – 5x = 2x = 2 × 60 = 120
Hence, Option B is correct.

MCQ: Ratio and Proportion - 1 - Question 15

The students in three classes are in the ratio 2 : 3 : 5 respectively. If 80 students are increased in each class, the ratio becomes 3 : 4 : 6. What was the initial number of students in all three classes together?

Detailed Solution for MCQ: Ratio and Proportion - 1 - Question 15

Let the number students in 2 classes = 2x, 3x and 5x

8x + 320 = 9x + 240
x = 80
So the answer = 2x + 3x + 5x = 10x = 10 × 80 = 800
Hence, Option A is correct.

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## Quantitative Aptitude for SSC CGL

314 videos|170 docs|185 tests