If a sum of money becomes Rs. 6,000 in 3 years and Rs. 10,500 in 7 years and 6 months at the same rate of simple interest. then what is the rate of interest?

Correct option is A

Simple interest for 4.5 years = 10500 - 6000 = 4500
Simple interest for 1 years = 4500/4.5 = 1000 
Simple interest for 3 years = 1000 × 3 = 3000
6000 = 3000 + P
P = 3000 
3000 = (3000 × R × 3 )/100
R = 100/3 = 33⅓%