Two numbers are in the ratio of 7 ∶ 8. If the difference between the numbers is 30, then find the numbers.

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UGC NET Paper 1: Held on 8th Oct 2022 Shift 1
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  1. 215, 245
  2. 205, 235
  3. 220, 250
  4. 210, 240

Answer (Detailed Solution Below)

Option 4 : 210, 240
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UGC NET Paper 1: Held on 21st August 2024 Shift 1
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50 Questions 100 Marks 60 Mins

Detailed Solution

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Given:

Two numbers are in the ratio of 7 ∶ 8. If the difference between the numbers is 30

Calculation:

Let the two numbers be 7x and 8x (since they are in the ratio of 7 : 8)

According to the problem, their difference is 30. Therefore, we can write:

8x - 7x = 30

x = 30

So the first number is:

7x = 7 × 30 = 210

And the second number is:

8x = 8 × 30 = 240

Therefore, the two numbers are 210 and 240.

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