the difference between ci and si on a certain sum p for 2 years at the rate a% per anum is
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Step-by-step explanation:
ANSWER
Given : n=2 years, R=7
2
1
=
2
15
S.I.−C.I.=360 ....... (i)
S.I. =
100
P×n×R
=
100
P×2×
2
15
=
100
15P
Amount (A)=P(1+
100
R
)
n
=P(1+
2×100
15
)
2
=P(1+
40
3
)
2
C.I. =A−P
=P(1+
40
3
)
2
−P
=P(1+
1600
9
+
40
2×3
−1)
=P(
1600
9
+
40
6
)
C.I.=P(
1600
249
) ........ (ii)
It is given that,
∣S.I.−C.I.∣=360
⟹
∣
∣
∣
∣
∣
100
15P
−P(
1600
249
)
∣
∣
∣
∣
∣
=360
⟹
1600
9P
=360
⟹P=64000
Hence, the sum is Rs. 64,000.
Verification :-
S.I. =
100
P×n×R
=
2×100
64000×2×15
=9600
C.I. =P[(1+
100
R
)
n
−1]
=64000[(1+
2×100
15
)
2
−1]
=9960
∣S.I.−C.I.∣=∣9600−9960∣=360
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