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UGC-NET-Paper1

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Two numbers are in the ratio 5 : 6. If 8 is subtracted from each number, then the ratio becomes 4 : 5. The two numbers are respectively:

1. 40, 48
2. 32, 40
3. 48, 40
4. 35, 42

दो संख्याएं 5: 6 के अनुपात में हैं। यदि प्रत्येक संख्या से 8 घटाया जाता है, तब यह अनुपात 4:5 हो जाता है। दोनों संख्याएं क्रमशः हैं:

1. 40, 48
2. 32, 40
3. 48, 40
4. 35, 42

This Question came in

UGC-NET-Linguistics-10-January-2025-Shift-2-Q40

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Detailed Explanation & Answer

### Step 1: Define Variables
Let the two numbers be **5x** and **6x**.

### Step 2: Form the Equation
After subtracting 8 from each number, the ratio becomes **4:5**.

So,

(5x - 8) / (6x - 8) = 4 / 5

### Step 3: Solve for x
Cross multiply:

(5x - 8) × 5 = (6x - 8) × 4

25x - 40 = 24x - 32

25x - 24x = 40 - 32

x = 8

### Step 4: Find the Numbers
First number = 5 × 8 = 40
Second number = 6 × 8 = 48

### Final Answer:
**(1) 40, 48**

The Correct Answer is 1

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