Ratio and Proportion - 1 - Free MCQ Practice Test with solutions, SSC CGL

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

Let the initial number boys = 5x
The initial number of girls = 3x
(5x – 80) = (3x + 40)
2x = 120
x = 60
So the answer = 300
Hence, Option C is correct.

Hence, Option A is correct.

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.

Let the quantity of mixed water:

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

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

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.

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.

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.

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

Given:
a : b = 5 : 9
b : c = 5 : 3

To find a : c

Make the common term b equal.

LCM of 9 and 5 = 45

Multiply first ratio by 5:

a : b = 5 : 9 = 25 : 45

Multiply second ratio by 9:

b : c = 5 : 3 = 45 : 27

Now,

a : b = 25 : 45
b : c = 45 : 27

Therefore,

a : c = 25 : 27

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.

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.

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.

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.