With a given rate of simple interest, the ratio of principle and amount for a certain period of time is $4 : 5$ . After $3$ years, with the same rate of interest, the ratio of the principle and amount becomes $5 : 7$ , The rate of interest per annum is

4 %

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5 %

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6 %

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7 %

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Solution

The correct option is B $5 %$
Suppose after $t$ years, $P =$ Rs. $4 x$ and Amount $=$ Rs. $5 x$
$\Rightarrow$ $P +$ S.I. after $t$ years $=$ Rs. $5 x$ .....(i)
Also, given $P$ : $[P +$ S.I.] after $(t + 3)$ years $= 5 : 7 = 1$ : $\frac{7}{5} = 4 x : \frac{7}{5} \times 4 x = 4 x : \frac{28 x}{5}$
$\Rightarrow$ P + S.I. after (t + 3) years = Rs $\frac{28 x}{5}$ .....(ii)
$∴$ Eq (i) - Eq (ii) gives
S.I. after 3 years $=$ Rs $(\frac{28 x}{5} - 5 x) = R s \frac{3 x}{5}$
$∴$ Rate of interest = $\frac{\frac{3 x}{5} \times 100}{4 x \times 3} = 5 %$ p.a.

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With a given rate of simple interest, the ratio of principle and amount for a certain period of time is 4:5. After 3 years, with the same rate of interest, the ratio of the principle and amount becomes 5:7, The rate of interest per annum is

With a given rate of simple interest, the ratio of principle and amount for a certain period of time is $4 : 5$ . After $3$ years, with the same rate of interest, the ratio of the principle and amount becomes $5 : 7$ , The rate of interest per annum is