Question

9
1. Two numbers are such that the ratio between them is 9:11. If the first number is decreased by 1 and the
second number is increased by 1, the ratio between the new numbers so formed is 7:9. Find the original
numbers.​

Answer 1

Given:-

• Two numbers are such that the ratio between them is 9 :11.
• If the first number is decreased by 1 and the second number is increased by 1.
• The ratio become 7 :9.

To Find:-

• To find the original number = ?

Solution:-

Let the first no. be 9x.

Let the second no. be 11x.

Now, we had to say in the 9 :11 .The first number is decreased by 1 and the second number is increased by 1 and it becomes 7 :9.

According to the question:

$\sf \implies\frac{9x - 1}{11x + 1} = \frac{7}{9} \\ \\ \sf \implies \: 9(9x - 1) = 7(11x + 1) \\ \\ \sf \implies \: 81x - 9 = 77x + 7 \\ \\ \sf \implies \: 81x - 77x = 7 + 9 \\ \\ \sf \implies \: 4x = 16 \\ \\ \sf \implies \: x = 4$

Hence, x is equal to 4.

Original number:

1. First number is = 9x = 9× 4 = 36
2. Second number is = 11x = 11 × 4 = 44

Answer 2

Step-by-step explanation:

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