A money lender finds that due to a fall in the annual rate of interest from 10% to 8
4
3
​
%, his year's income diminishes by Rs. 84.50. Find his capital.

Let the capital be P.
The initial annual rate of interest is R
1
​
=10%.
The new annual rate of interest is R
2
​
=8
4
3
​
%=8.75%.

The decrease in the rate of interest is:

ΔR=10%−8.75%=1.25%
This decrease in the percentage rate corresponds to a decrease of Rs. 84.50 in annual income:

1.25% of P=84.50
100
1.25
​
×P=84.50
P=
1.25
84.50×100
​

P=
1.25
8450
​
=
5
8450×4
​
=1690×4=Rs. 6,760