1/2 of a certain sum is lent at 20 percent rate of interest, 2/5 of the remaining sum is lent at 25 percent rate of interest. The remaining sum is lent at 10 percent rate of interest. If the simple interest received on the total sum for 2 years is Rs. 360, then what is the sum ?

Rs. 1000

Simple Interst for 2 years = Rs 360

Simple Interst for 1 years = Rs 180 

ATQ 

Simple Interest = P\(\frac{1}{2}\) × 20%  +  P\(\frac{1}{2}\)\(\frac{2}{5}\) × 25% +  P[\(\frac{1}{2}\)\(\frac{3}{5}\)] × 10%

                        = P{10% + 5% + 3%}

                        = P {18%}

Here,

18% P = Rs.180

∴ Principal = Rs 1000