Question
The denominator of a rational number is greater than its numerator by 3. If the numerator is increased by 7 and the denominator is decreased by 1, then the new number becomes 32. Find the original number.
Answer: Option A
:
A
Let the numerator of a rational number be x.
Then the denominator of a rational number would be (x+3).
When the numerator is increased by 7, it becomes (x+7)
When the denominator is decreased by 1, it becomes
⇒x+3−1=x+2
The new number formed =32
So,(x+7)(x+2)=322x+14=3x+63x−2x=14−6x=8
∴ Numerator, x=8
Denominator, x+3=8+3=11
Hence, the original rational numberis 811
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:
A
Let the numerator of a rational number be x.
Then the denominator of a rational number would be (x+3).
When the numerator is increased by 7, it becomes (x+7)
When the denominator is decreased by 1, it becomes
⇒x+3−1=x+2
The new number formed =32
So,(x+7)(x+2)=322x+14=3x+63x−2x=14−6x=8
∴ Numerator, x=8
Denominator, x+3=8+3=11
Hence, the original rational numberis 811
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