Question

The ratio between two numbers is 7:9 if each number is increased by 44 then the ratio becomes 11:13 find their difference.

Answer 1

❍Let's say that first number be 7x and second number be 9x respectively.

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• As we are provided that the ratio between two numbers is 7:9. If each number is increased by 44 then the ratio becomes 11:13.Find their difference.

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$\: \: \: \sf \: : \implies \: \frac{7x + 44}{9x + 44} = \frac{11}{13} \\ \\ \\ \: \: \: \sf \: : \implies \: 13(7x + 44) = 11(9x + 44) \\ \\ \\ \: \: \: \sf \: : \implies \: 91x + 572 = 99x + 484 \\ \\ \\ \: \: \: \sf \: : \implies \: 99x - 91x = 572 - 484 \\ \\ \\ \: \: \: \sf \: : \implies \: 8x = 88 \\ \\ \\ \: \: \: \sf \: : \implies \: x = \cancel\frac{88}{8} \\ \\ \\ \: \: \: \sf \: : \implies \: x = 11$

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$\: \: \sf \: 1st \: number = 7x \\ \\ \sf= 7 \times 11 \\ \\ \sf= 77 \\ \\ \: \: \sf \: 2nd \: number = 9x \\ \\ \sf= 9 \times 11 \\ \\ \sf= 99$

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Required difference = 99 - 77 = 22.

Answer 2

Given that:

• The ratio between two numbers is 7 : 9.
• Each number is increased by 44 then the ratio becomes 11 : 13.

To Find:

• Their difference.

Let us assume:

• One number be 7x.
• Other number be 9x.

Finding the value of x:

According to the question.

⟶ (7x + 44)/(9x + 44) = 11/13

Cross multiplication.

⟶ 13(7x + 44) = 11(9x + 44)

⟶ 91x + 572 = 99x + 484

⟶ 99x - 91x = 572 - 484

⟶ 8x = 88

⟶ x = 88/8

⟶ x = 11

∴ The value of x = 11

Finding their difference:

⟶ Difference = 9x - 7x

⟶ Difference = 2x

Substituting the value of x.

⟶ Difference = 2 × 11

⟶ Difference = 22

Hence,

• Their difference is 22.