The S.I on a certain sum of money for 3 years at 8% per annum is half the C.I on Rs. 4000 for 2 years at 10% P.a. the sum placed on S.I is
A) Rs. 1550
B) Rs. 1750
C) Rs. 1650
D) Rs. 2000
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Correct explanation is required
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Answers & Comments
Step-by-step explanation:
For Simple Interest (S.I):
Principal amount = P
Time = 3 years
Rate = 8% per annum
For Compound Interest (C.I):
Principal amount = Rs. 4000
Time = 2 years
Rate = 10% per annum
The formula for Simple Interest is:
Simple Interest (S.I)
=
�
×
�
×
�
100
Simple Interest (S.I)=
100
P×R×T
The formula for Compound Interest is:
Compound Interest (C.I)
=
�
(
1
+
�
100
)
�
−
�
Compound Interest (C.I)=P(1+
100
R
)
T
−P
Given that the S.I is half the C.I and we need to find the principal amount for S.I, let's start with the calculation for C.I:
C.I
=
�
(
1
+
�
100
)
�
−
�
C.I=P(1+
100
R
)
T
−P
C.I
=
4000
×
(
1
+
10
100
)
2
−
4000
C.I=4000×(1+
100
10
)
2
−4000
C.I
=
4000
×
(
1.1
)
2
−
4000
C.I=4000×(1.1)
2
−4000
C.I
=
4000
×
1.21
−
4000
C.I=4000×1.21−4000
C.I
=
4840
−
4000
C.I=4840−4000
C.I
=
840
C.I=840
Now, we're given that the S.I is half the C.I:
S.I
=
C.I
2
S.I=
2
C.I
S.I
=
840
2
S.I=
2
840
S.I
=
420
S.I=420
Let's use the formula for S.I to find the principal amount for S.I:
S.I
=
�
×
�
×
�
100
S.I=
100
P×R×T
420
=
�
×
8
×
3
100
420=
100
P×8×3
420
=
24
�
100
420=
100
24P
�
=
420
×
100
24
P=
24
420×100
�
=
1750
P=1750
Therefore, the principal amount placed on Simple Interest is Rs. 1750 (Option B).
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