Simple interest on a certain sum of money for 3 years at 14% per annum is half the compound interest on Rs 10000 for 2 years at 10% per annum. The sum placed on simple interest is:

First, let us find the compound interest (CI) on Rs 10000 for 2 years at 10% per annum.
Amount (A)=P(1+
100
R
​
)
t

A=10000(1+
100
10
​
)
2
=10000×(
10
11
​
)
2

A=10000×
100
121
​
=12100
CI=A−P=12100−10000=Rs 2100
According to the question, the simple interest (SI) is half of this compound interest:

SI=
2
1
​
×2100=Rs 1050
Now, we calculate the principal sum (P
SI
​
) placed under simple interest for T=3 years at R=14% per annum:

SI=
100
P
SI
​
×R×T
​

1050=
100
P
SI
​
×14×3
​

1050=
100
42⋅P
SI
​

​

P
SI
​
=
42
1050×100
​
=
42
105000
​
=2500
The sum placed on simple interest is Rs 2500.