Numerator of a rational number is three less than its denominator. If 5 is added to both numerator and denominator, than it results to 3/4. Find the number.
Answers
Let the numerator and denominator of the number be x and y respectively.
According to the question,
☛ Numerator is three less than the denominator
☛ x = y - 3 ...(1)
Also,
☛ If 5 is added to both the numerator and denominator then the number becomes 3/4
☛ (x + 5) / (y + 5) = 3/4
☛ 4(x + 5) = 3(y + 5)
☛ 4x + 20 = 3y + 15
☛ 4x - 3y = -5
Put x = y - 3 { from eq.(1) }
☛ 4(y - 3) - 3y = -5
☛ 4y - 12 - 3y = -5
☛ 4y - 3y = 12 - 5
☛ y = 7
Putting value of y in (1)
☛ x = y - 3
☛ x = 7 - 3
☛ x = 4
Number = Numerator / Denominator
☛ number = x / y
☛ number = 4/7
Hence, The required number is 4/7
Answer:
the rational no.is 4/7.
let the denominator=x
and given that numerator (3 less than denominator)=x-3
According to the question
when 5is added to both numerator and denominator the rational number becomes 3/4
new numerator=x+2
and new denominator=x+5
on solving we get
x+2/x+5=3/4
4x+8=3x+15
4x-3x=15-8
x=7
therefore rational number=4/7