The  sequence of coloured bands in two carbon resistors R₁ and R₂ is (1) brown, green , blue and (2) orange, black and green.Find the ratio of the currents  flowing through them, when connected in parallel to a 15 V battery

Hello!

The resistance of R1 would be 15 X 10⁶ ohms. 

The resistance of R2 would be 3 X 10⁶ ohms. 

and the potential difference (V) is 15V

Now, according to the Ohm's Law, the respective current would be

 I1 = V/R1 and I2 = V/R2

so  I1 = 15/15 X 10⁶ = 1 μA  [1μA = 10^-6 A]

and  I2 = 15/3 X 10⁶ = 5 μA

finally, 

the ratio of the currents flowing through would be

 I2 = 5*I1  or  I2/I1 = 5  

For more on resistor color codes, please refer to the following link

 Resistor Color Codes Chart