Question

the numerator and denominator of a rational number are in the ratio 3:4. If 3 is subtracted from the numerator and 2 is added to its denominator, the new number becomes 1/5. Find the rational number

Answer 1

Let the ratio of numerator and denominator be X:Y.
Therefore,
X:Y = 3:4
4X= 3Y
4X-3Y = 0
X= 3Y/4.......(1)
A/Q,
X-3/Y+2 = 1/5
5(X-3) = 1(Y+2)
5X-15 =Y+2
5X-Y = 2+15
5X-Y = 17
Put X = 3Y/4 in,
5X-Y = 17
5×3Y/4-Y = 17
15Y/4-Y = 17
15Y-4Y = 17
11Y = 17
Y = 17/11.
Therefore,
X = 3Y/4
= 3×17/11/4 = 51/11/4 = 204/11