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Question

The denominator of a rational number is greater than its numerator by 8.

If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 32.

Find the rational number.


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Solution

Step 1:Assuming the rational number

Let the numerator of the rational number be x.

Therefore by the given condition denominator =x+8

Hence the rational number is xx+8

Step 2.Finding the rational number.

According to question If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 32

Therefore we have

,x+17x+8-1=32

x+17x+7=322(x+17)=3(x+7)2x+34=3x+212x-3x=21-34-x=-13x=13

Hence the numerator is 13.

Now the denominator =x+8

=13+8=21

Hence, the rational number is 1321.


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