If the compound interest on a certain sum of money for 2 years is Rs. 2700 and the simple interest on the same sum for the same period and for same rate of interest is 1250, then rate % =
(a.) 232 %
(b.) 250 %
(c.) 220 %
(d.) 450 %
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Let the sum of money be
′
x
′
.
T=2 years
C.I=2700. , Rate=R
A=P(1+
100
R
)
2
⇒
(x+2700)=x(1+
100
R
)
2
⟶(I)
Now,
S.I=2500
⇒2500=
100
x×R×2
⇒
xR=125000
⇒
R=
x
125000
→(II)
Putting
′
x
′
in eq (I)
(
R
125000
+2700)=
R
125000
(1+
100
R
)
2
⇒(
R
125000+2700R
)=
R
125000
(1+
100
R
)
2
⇒(125000+2700R)=125000(1+
100
R
)
2
⇒1250+27R=1250(1+
100
R
)
2
⇒1250+27R=1250(1+2(0.0R)+(0.0R)
2
)
⇒1250+27R=1250+25R+0.125R
2
⇒0.125R
2
−2R=0
⇒R(0.125R−2)=0
⇒R=0 or 0.125R−2=0
But R can't be 0.
∴0.125R−2=0
⇒R=
0.125
2
=16
∴
R=16
%
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