Simple interest on a certain sum of money for 3 years at 10% per annum is half the compound interest on Rs 6000 for 2 years at 10% per annum. The sum placed on simple interest is:

First, let's calculate the compound interest (CI) on Rs 6000 for 2 years at 10% per annum.
The formula for the amount under compound interest is:

A=P(1+
100
R
​
)
t

A=6000(1+
100
10
​
)
2
=6000×(
10
11
​
)
2

A=6000×
100
121
​
=60×121=Rs 7260
So, the compound interest is:

CI=A−P=7260−6000=Rs 1260
According to the question, the simple interest (SI) on a certain sum is half of this compound interest:

SI=
2
1
​
×1260=Rs 630
Let the principal sum for the simple interest be P
s
​
. The time period is t=3 years and the rate of interest is R=10%.

SI=
100
P
s
​
×R×t
​

630=
100
P
s
​
×10×3
​

630=
100
30P
s
​

​

630=
10
3P
s
​

​

3P
s
​
=6300
P
s
​
=Rs 2100
Thus, the sum placed on simple interest is Rs 2100.