An amount of Rs. 12,000 was borrowed at some rate of simple interest. After four months, Rs. 6,000 more were added to it and the rate of interest on the total principal was doubled from the previous rate. At the end of the year, Rs. 2,800 was paid as interest, calculate the rate of interest initially charged?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Let, Rate}} = 12x\% {\text{ per year}} \cr & \frac{{12000 \times 4x}}{{100}} + \frac{{18000 \times 16x}}{{100}} = 2800 \cr & 480x + 2880x = 2800 \cr & 3360x = 2800 \cr & x = \frac{{10}}{{12}} \cr & {\text{Rate}} = 12x \cr & = \frac{{10}}{{12}} \times 12 \cr & = 10\% \cr} $$