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Mathematics

Two numbers are in the ratio 7 : 11. If 7 is added to each of the numbers, the ratio becomes 2 : 3. The smaller number is:

  1. 39

  2. 49

  3. 66

  4. 77

Ratio Proportion

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Answer

Let the two numbers be 7x and 11x.

Given,

When 7 is added to each number, the new ratio is 2 : 3.

7x+711x+7=23\therefore \dfrac{7x + 7}{11x + 7} = \dfrac{2}{3}

⇒ 3(7x + 7) = 2(11x + 7)

⇒ 21x + 21 = 22x + 14

⇒ 22x - 21x = 21 - 14

⇒ x = 7.

The smaller number is 7x = 7(7) = 49.

Hence, option 2 is the correct option.

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