A person invests money in three different schemes for 6 years, 10 years and 12 years at 10 percent, 12 percent and 15 percent simple interest respectively. At the completion of each scheme, he gets the same interest. The ratio of his investment is

Let the three amounts be Rs. x, Rs. y and Rs. z,
Then,
$$\eqalign{ & \frac{{x \times 10 \times 6}}{{100}} = \frac{{y \times 12 \times 10}}{{100}} = \frac{{z \times 15 \times 12}}{{100}} \cr & \Rightarrow 60x = 120y = 180z \cr & \Rightarrow x = 2y = 3z = k(say) \cr & \Rightarrow x = k,y = \frac{k}{2},z = \frac{k}{3} \cr & \Rightarrow x:y:z = k:\frac{k}{2}:\frac{k}{3} \cr & \Rightarrow x:y:z = 1:\frac{1}{2}:\frac{1}{3} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 6:3:2 \cr} $$