Question

Two numbers are in the ratio 5:9. On subtracng 3 from each, the ratio becomes 1:2. Find the numbers.

Answer 1

Given :-

• Two numbers are in the ratio 5:9
• On subtracting 3 from each, the ratio becomes 1:2.

To find :-

• The numbers.

Solution :-

Let the two numbers be 5x and 9x

↬ $\sf \dfrac{5x - 3}{9x - 3} = \dfrac{1}{2}$

By cross multiplication,

↬ 2(5x - 3) = 9x - 3

↬ 10x - 6 = 9x - 3

↬ 10x - 9x = -3 + 6

↬ x = 3

Therefore, The numbers are :-

• 5x = 5 × 3 = 15
• 9x = 9 × 3 = 27

Verification:

↬ $\sf \dfrac{5x - 3}{9x - 3} = \dfrac{1}{2}$

↬ 2(5(3) - 3) = 9(3) - 3

↬2(15 - 3) = 27 - 3

↬30 - 6 = 27 - 3

↬24 = 24

Answer 2

Given :

• Two numbers are in the ratio 5:9
• On subtracng 3 from each, the ratio becomes 1:2.

To Find :

• The Numbers

Solution :

⟶ Let the First number be 5x

⟶ Let the Second number be 9x

✰ After Substraction of 3 :

⟶ First number will be 5x - 3

⟶ Second number will be 9x - 3

According to the Question :

⟹ 5x - 3 / 9x - 3 = 1/2

⟹ 2 (5x - 3) = 1 (9x - 3)

⟹ 10x - 6 = 9x - 3

⟹ 10x - 9x = 6 - 3

⟹ x = 3

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Verification :

➞ 5x - 3 / 9x - 3 = 1/2

➞ 2 (5x - 3) = 1 (9x - 3)

➞ 10x - 6 = 9x - 3

➞ 10 × 3 - 6 = 9 × 3 - 3

➞ 30 - 6 = 27 - 3

➞ 24 = 24

Hence Verified

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Therefore :

• First Number = 5x = 5 × 3 = 15
• Second Number = 9x = 9 × 3 = 27

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