16. The numerator of a fraction is 7 less than the
denominator. If 3 is added to the numerator
and 2 is added to the denominator, the value
2
of the fraction becomes Find the original
3
fraction.
ş. Find the original
Answers
Correct Question:-
Solution:-
Let the numerator be x and
the denominator be y
Given,
The numerator of a fraction is 7 less than the denominator.
x + 7 = y ..... 1
If 3 is added to the numerator and 2 is added to the denominator, the value becomes 2/3.
️ ➭ ( x + 3 ) / ( y + 2 ) = 2/3
️ ➭
️ ➭
️ ➭
️ ➭
️ ➭
️ ➭
️ ➭
Then,
The denominator is
️ ➭
️ ➭
️ ➭
The fraction is
The numerator of a fraction is 7 less than the denominator. If 3 is added to the numerator and 2 is added to the denominator, the value of the fraction becomes 2/3. Find the original fraction.
- Numerator of the fraction is 7 less than the denominator.
- The value of the fraction becomes 2/3 when 3 is added to the numerator and 2 is added to the denominator.
- The original fraction.
Let:-
- The numerator = x
- The denominator = y
Since,
Numerator of the fraction is 7 less than the denominator.
∴ y - 7 = x
⇒ y = x + 7
Since,
The value of the fraction becomes 2/3 when 3 is added to the numerator and 2 is added to the denominator.
∴
⇒ 3(x + 3) = 2(y + 2)
⇒ 3x + 9 = 2y + 4
⇒ 3x + 9 = 2(x + 7) + 4
⇒ 3x + 9 = 2x + 14 + 4
⇒ 3x - 2x = 18 - 9
⇒ x = 9
∴ the numerator = x = 9
∴ the denominator = y = x + 7 = 9 + 7 = 16
∴ the original fraction =