The simple interest on a sum of money is frac | vedclass

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Question

(B) Let the principal be $P$,the rate of interest be $R = x \%$,and the time be $T = x$ years.The formula for simple interest is $SI = \frac{P 	imes

Vedclass · Accepted Answer

$6 \frac{2}{3} \%, 6$ years $8$ months

Vedclass · Answer

(B) Let the principal be $P$,the rate of interest be $R = x \%$,and the time be $T = x$ years.The formula for simple interest is $SI = \frac{P 	imes R 	imes T}{100}$.Given that $SI = \frac{4}{9} P$,we substitute the values:$\frac{4}{9} P = \frac{P 	imes x 	imes x}{100}$Dividing both sides by $P$:$\frac{4}{9} = \frac{x^2}{100}$Solving for $x^2$:$x^2 = \frac{400}{9}$$x = \sqrt{\frac{400}{9}} = \frac{20}{3} = 6 \frac{2}{3}$.Therefore,the rate is $6 \frac{2}{3} \%$ and the time is $6 \frac{2}{3}$ years.To convert $6 \frac{2}{3}$ years into years and months:$6$ years $+ (\frac{2}{3} 	imes 12)$ months $= 6$ years and $8$ months.

The simple interest on a sum of money is $\frac{4}{9}$ of the principal. Find the rate per cent and time,if both are numerically equal.

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