Q 34 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 3/2. Find the rational number. 035 Five years before the age of Neerai and Neera was in the ratio 4:5 The ratio of their present ages is 5:6. Find their present ages.
Answers
Answer:
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 3/2. Find the rational number.
Answer:
Let the numerator of the rational number be x.
So as per the given condition, the denominator will be x + 8.
The rational number will be \(\frac{x}{x+8}\)
According to the given condition,
\(\frac{x+17}{x+8-1} = \frac{3}{2}\)
\(\frac{x+17}{x+7} = \frac{3}{2}\)
3(x + 7) = 2(x + 17)
3x + 21 = 2x + 34
3x – 2x + 21 – 34 = 0
x – 13 = 0
x = 13
The rational number will be
= \(\frac{x}{x+8}\)
= \(\frac{13}{13+8}\)
Rational number = 13/21
Step-by-step explanation:
Answer:
Answer 1
Given:
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 3/2.
Solution:
Let the numerator be x.
Therefore, the denominator would be x + 8
Now, ATQ.
(x + 17) / (x + 8 - 1) = 3/2
=⟩ (x + 17) / (x + 7) = 3/2
=⟩ 2(x + 17) = 3(x + 7)
=⟩ 2x + 34 = 3x + 21
=⟩ 2x - 3x = 21 - 34
=⟩ -x = -13
=⟩ x = 13
Therefore, the required fraction is
x / x + 8
= 13 / (13 + 8)
= 13/21 (Ans)
Answer 2
Given:
Ratio of the ages of Neeral and Neera, 5 yrs ago was 4:5.
Ratio of their present ages = 5:6
Solution:
Let Neeral and Neera's age be 4x and 5x respectively 5 yrs ago.
Therefore, their present ages would be
Neeral = 4x + 5
Neera = 5x + 5
Now, ATQ.
(4x + 5) / (5x + 5) = 5/6
=⟩ 6(4x + 5) = 5(5x + 5)
=⟩ 24x + 30 = 25x + 25
=⟩ 24x - 25x = 25 - 30
=⟩ -x = -5
=⟩ x = 5
Present ages of:
Neeral = 4x + 5
= 4 × 5 + 5
= 25yrs
Neera = 5x + 5
= 5 × 5 + 5
= 29yrs
Hope this helped you, cheers :)