Some part of Rs 9500 was lent at the rate of 15% per annum simple interest and the remaining part at the rate of 20% per annum simple interest. The total interest received after
2
3
​
years is Rs 2565. What is the ratio of money lent at the rate of 15% and 20%?

Let the amount lent at 15% be P
1
​
and the amount lent at 20% be P
2
​
.
Total principal P=P
1
​
+P
2
​
=9500.
Total time T=
2
3
​
years.
Total Interest = Rs 2565.

First, let's find the overall effective annual interest rate (R):

Total Interest=
100
P×R×T
​

2565=
100
9500×R×
2
3
​

​

2565=95×R×1.5
2565=142.5×R
R=
142.5
2565
​
=18%
Now, applying the rule of Alligation:

Rate of Part 1 (R
1
​
) = 15%

Rate of Part 2 (R
2
​
) = 20%

Mean Rate (R) = 18%

P
2
​

P
1
​

​
=
R−R
1
​

R
2
​
−R
​
=
18−15
20−18
​
=
3
2
​

Thus, the ratio of money lent at 15% and 20% is 2:3.