Question

in a fraction the numerator and the denominator are in the ratio 3:5 if 9 is added to both the numerator and the denominator then tjey are in the ration 15:22. What is the fraction. Solve algebraically​

Answer 1

Let the ratio of the fraction be 3x & 5x

Let the ratio of the fraction be 3x & 5xNumber to be get added = 9

then,

3x+9 : 5x+9

3x+9 : 5x+9New fraction formed = 15:22

A/Q,

3x+9/5x+9 = 15/22

3x+9/5x+9 = 15/22or, 22(3x+9) = 15(5x+9) (Cross multiplication)

3x+9/5x+9 = 15/22or, 22(3x+9) = 15(5x+9) (Cross multiplication) or, 66x+198 = 75x+135

3x+9/5x+9 = 15/22or, 22(3x+9) = 15(5x+9) (Cross multiplication) or, 66x+198 = 75x+135or, 66x-75x = 135-198

3x+9/5x+9 = 15/22or, 22(3x+9) = 15(5x+9) (Cross multiplication) or, 66x+198 = 75x+135or, 66x-75x = 135-198or, -9x = -63

3x+9/5x+9 = 15/22or, 22(3x+9) = 15(5x+9) (Cross multiplication) or, 66x+198 = 75x+135or, 66x-75x = 135-198or, -9x = -63or, x = (-63) ÷(-9) = 7

Therefore,

Numerator = 3x = 3×7 = 21

Numerator = 3x = 3×7 = 21and, Denominator = 5x = 5×7 = 35

Numerator = 3x = 3×7 = 21and, Denominator = 5x = 5×7 = 35Required fraction = 21/35