A certain sum in simple interest becomes 6500 in 3 years and 7500 in 5 years. Find the principal and rate of interest?
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Answer:
Let the initial amount of money be P.
A=P(1+
100
R
)
T
where R= Rate of Interest and T= Time period.
Amount after 3 years =6500
⇒6500=P(1+
100
R
)
3
⟶(I)
Amount after 6 years =10,562.5
⇒10562.5=P(1+
100
R
)
6
⟶(II)
From eq(I),
P
6500
=(1+
100
R
)
3
⇒(
P
6500
)
2
=(1+
100
R
)
6
⟶(III)
Putting eq(III) in eq(II)
10562.5=P(
P
6500
)
2
⇒10562.5=P×
P
2
(6500)
2
⇒P=
10562.5
(6500)
2
=4000
Hence, the initial amount of money is equal to Rs. 4000.
Step-by-step explanation:
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