The simple interest on a certain sum for 4
2
1
​
years at 10% p.a. is 60% of the compound interest on a sum of Rs. 12,000 for 1 year at 10% p.a., interest compounded half yearly. The sum on which the simple interest is calculated is:

1. Calculate the Compound Interest (CI):
Principal (P
CI
​
) = Rs. 12,000

Time = 1 year = 2 half-years

Rate = 10% p.a. = 5% per half-year

Amount (A)=12000×(1+
100
5
​
)
2
=12000×(
20
21
​
)
2
=12000×
400
441
​
=30×441=13,230
CI=13230−12000=Rs. 1,230
Calculate the Simple Interest (SI):

SI=60% of CI=
100
60
​
×1230=738

Calculate the Principal for Simple Interest (P
SI
​
):

Time (T) = 4
2
1
​
=
2
9
​
years

Rate (R) = 10% p.a.

SI=
100
P
SI
​
×R×T
​

738=
100
P
SI
​
×10×
2
9
​

​

738=
100
P
SI
​
×45
​

P
SI
​
=
45
738×100
​
=
45
73800
​
=1640
Therefore, the sum is Rs. 1,640.