The ratio of two numbers is 5 ∶ 9 . If 6 is added to the greater number and 6 is subtracted from smaller number, then greater number becomes 6 times the smaller number. What are the numbers?

This question was previously asked in
SSC MTS (2022) Official Paper (Held On: 02 May 2023 Shift 2)
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  1. 15 and 27
  2. 10 and 18
  3. 25 and 45
  4. 20 and 36

Answer (Detailed Solution Below)

Option 2 : 10 and 18
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SSC MTS 2024 Official Paper (Held On: 01 Oct, 2024 Shift 1)
90 Qs. 150 Marks 90 Mins

Detailed Solution

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Data:

Ratio of numbers = 5 ∶  9

Concept:

Solve the given equations to find the numbers.

Solution:

⇒ Let the numbers be 5x and 9x.

⇒ (9x + 6) = 6(5x - 6)

⇒ 9x + 6 = 30x - 36

⇒ 6 + 36 = 30x - 9x

⇒ 21x = 42

⇒ x = 2

⇒ The numbers are 5 × 2 = 10 and 9 × 2 = 18

Therefore, the numbers are 10 and 18.

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