A sum of money of Rs. 1000 is lent out in two parts in such a way that the interest on one part at 10% per annum for 5 years is equal to another at 5% for 10 years. Calculate the stun lent out at 5%.

Let one part of money is 'x' then 2nd part is 1000-x

Interest on first part is$$ I_1=\frac{P\times{R}\times{T}}{100}=\frac{{x}\times10\times5}{100}$$

$$I_1=0.5x$$

Similarly for 2nd part

Interest on 2nd part is$$ I_2=\frac{P\times{R}\times{T}}{100}=\frac{{1000-x}\times5\times10}{100}$$

$$I_2=\frac{1000-x}{2}$$

Given $$I_1=I_2$$

$$0.5x=\frac{1000-x}{2}$$

$$x+x=1000$$

$$x=500$$      1st part

$$1000-500=500$$ 2nd part