Shashikant derives an annual income of Rs. 668.25 from Rs. 10000 invested partly at 8% p.a. and partly at 5% p.a. simple interest. How much money is invested at 5%? (Arun Sharma QA, level-1)

If the entire amount was invested @5% and @8% the he would get Rs. 500 and Rs. 800 accordingly. Now apply alligations...
So the parts are in the ratio (668.58 - 500) : (800 - 668.58) = 131.42 : 168.58
Share of his investment @5% is 131.42 X 10000/(131.42 + 168.58) = 4380.667

Let x be the amount invested @8% and y be the amount invested @5%, so (x+y=10000) and (8% of x + 5% of y = 668.25). by solving these two equations you will get the value of y and that value will be your answer.

Please share the process

4391.667