Question !!
The denominator pf a rational number. is greater than its numerator by 5. If the numerator is increased by 11 and the denominator is descreased by 3 , the numerator obtained is 5/2 . Find the rational number
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Answers
Answer:
Let the numerator of the rational number =p
Then, the denominator of the rational number =p+5
When numerator is increased by 6, the new numerator =p+6
When denominator decreased by 3, the new denominator =p+2
According to the question,
p+2
p+6
=
3
5
⟹3p+18=5p+10
⟹2p=8
∴p=4
Numerator =p=4
Denominator=p+5=4+5=9
Original number =
9
4
Answer :
- Rational number is 4/9.
Given :-
- The denominator of a rational number. is greater than its numerator by 5. If the numerator is increased by 11 and the denominator is descreased by 3, the numerator obtained is 5/2.
To Find :-
- Find the rational number ?
Solution :-
- Denominator = Numerator + 5
- Number of rational number be x
- So, it's denominator will be = (x + 5).
★ According to the question :
- If the numerator is increased by 11 and the denominator is decreased by 3, the number obtained = 5/2
Therefore,
➻ (x + 11)/(x + 5 - 3) = 5/2
➻ (x + 11)/(x + 2) = 5/2
• Cross multiplication
➻ 2(x + 11) = 5(x + 2)
➻ 2x + 22 = 5x + 10
➻ 2x - 5x = 10 - 22
➻ -3x = -12
➻ x = -12/-3
➻ x = 12/3
➻ x = 4
- Hence, numerator of the required rational number is 4.
Now,
➻ Denominator = Numerator + 5
➻ Denominator = x + 5
• Putting values of 'x' in above eqⁿ,
➻ Denominator = 4 + 5
➻ Denominator = 9
- Hence, denominator of the required rational number is 9.
So,
- Rational number
➻ Numerator/Denominator
➻ 4/9
- Hence, the required rational number is 4/9.
Verification :-
- If the numerator is increased by 11 and the denominator is decreased by 3, the number obtained = 5/2
Therefore,
➻ (x + 11)/(x + 5 - 3) = 5/2
➻ (x + 11)/(x + 2) = 5/2
• Putting values of 'x' in above eqⁿ,
➻ (4 + 11)/(4+ 2) = 5/2
➻ 15/6 = 5/2
➻ 5/2 = 5/2
➻ LHS = RHS
- Hence, verified.
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