A sum of Rs. $1550$ was lent partly at $8 %$ p.a. simple interest. The total interest received after $3$ years was Rs. $300$ . The ratio of the money lent at $5 %$ to that of lent at $8 %$ is __________.

5 : 8

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8 : 5

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16 : 15

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31 : 6

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Solution

The correct option is B $16 : 15$
Let the money lent at $5 %$ $S I$ be $R s . x$
Interest on $R s . x$ for $3 y e a r s = \frac{P T R}{100} = \frac{x \times 3 \times 5}{100} = \frac{3 x}{20}$
Money lent at $8 %$ SI is $R s . (1550 - x)$
Interest on $R s . (1550 - x) = \frac{(1550 - x) \times 3 \times 8}{100} = \frac{6 (1550 - x)}{25}$
Given total interest $= R s .300$
$\Rightarrow$ $\frac{3 x}{20} + \frac{6 (1550 - x)}{25} = 300$

$\Rightarrow$ $\frac{15 x + 24 (1550 - x)}{100} = 300$

$\Rightarrow$ $15 x + 37200 - 24 x = 30000$
$\Rightarrow$ $37200 - 30000 = 9 x$
$\Rightarrow$ $9 x = 7200$
$∴$ $x = 800$
Hence money lent at $5 %$ SI is $R s .800$
Money lent at $8 %$ SI is $R s . (1550 - 800) = R s .750$
Thus the ratio of money lent at $5 %$ to that of money lent at $8 % = 800 : 750 = 16 : 15$

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A sum of Rs. 1550 was lent partly at 8% p.a. simple interest. The total interest received after 3 years was Rs. 300. The ratio of the money lent at 5% to that of lent at 8% is __________.

A sum of Rs. $1550$ was lent partly at $8 %$ p.a. simple interest. The total interest received after $3$ years was Rs. $300$ . The ratio of the money lent at $5 %$ to that of lent at $8 %$ is __________.