The denominator of a rational number is greater than its numerator by 5.If the numerator is decreased by 20and the denominator is increased by 3 ,the number obtained is 1/3 . find the rational number
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Answer:
decreased by 20and the denominator is increased by 3 ,the number obtained is 1/3 . find the rational number
Given:-
- Denominator of a rational number is greater than its numerator by 5.
- If the numerator is decreased by 20 and the denominator is increased by 3, the number obtained is 1/3.
To Find:-
- The rational number.
Assumption:-
- Let the numerator be x
- denominator = (x + 5)
Solution:-
Its given that if the numerator is decreased by 20 and the denominator is increased by 3, the number obtained will be 3.
Hence,
Numerator decreased by 20,
- (x - 20)
Denominator increased by 3
- (x + 5 + 3) = (x + 8)
According to the problem,
= (x - 20)/(x + 8) = 1/3
By cross multiplication:-
⇒ 3(x - 20) = 1(x + 8)
⇒ 3x - 60 = x + 8
⇒3x - x = 60 + 8
⇒ 2x = 68
⇒ x = 68/2
⇒ x = 34
∴ The value of x = 34
Let us put the value of x in the assumption:-
- Numerator = x = 34
- Denominator = x + 5 = 34 + 5 = 39.
∴ The rational number is 34/39.
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Verification:-
Let us see if the numerator is decreased by 20 and denominator is increased by 3 then, the rational number becomes 1/3 or not.
Numerator decreased by 20
- 34 - 20 = 14
Denominator increased by 3
- 39 + 3 = 42
Rational number:-
- 14/42 = 1/3
Hence Verified!!!
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