Question

A certain amount of money amounts to rs 4400 in 2 yrs and to rs 4600 in 3 yrs. Find the principal and the rate of interest

Answer 1

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$\underline{\underline{\huge{\textbf{Solution:}}}}$

Given,
A certain amount of money amounts to rs 4400 in 2 yrs and to rs 4600 in 3 yrs.

$\underline{\large{\textsf{Step-1:}}}$
Find Simple Interest for 1 year

$S.I\: for\: 1\: year = Amount\: after\: 2\: years - Amount\: after\: 3 years$

$\implies S.I\: for\: 1\: year = 4600 - 4400$

$\implies S.I\: for\: 1\: year =Rs.\: 200$

$\underline{\large{\textsf{Step-2:}}}$
Find the Simple Interest for 2 years

$S.I\: for\: 2\: year = 2 \times S.I\: for\: 1\: year$

Substitute value

$\implies S.I\: for\: 2\: year = 2 \times 200$

$\implies S.I\: for\: 2\: year = Rs.\: 400$

$\therefore$
For first two years, Simple Interest = Rs. 400

$\underline{\large{\textsf{Step-3:}}}$
Find principal (or) the sum

$Principal = Amount\: after\: 2\: years - Simple\: Interest$

Substituting Values

$\implies Principal = 4400 - 400$

$\implies Principal = Rs. 4400$

$\underline{\large{\textsf{Step-4:}}}$
Find Rate of Interest

We have,
Simple Interest $S.I = \dfrac{P \times T \times R}{100}$

$\implies R = \dfrac{100 \times S.I}{P \times T}$

Substituting Values

$\implies R = \dfrac{100 \times 400}{4000 \times 2}$

$\implies R = \dfrac{40000}{8000}$

$\implies R = 5\%$

$\therefore$

$\star Simple\: Interest = Rs. 400$

$\star Rate\: of\: Interest = 5 \%$

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Answer 2

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