Question

Two friends meena and tina invested equals sums of money for 2 years at 16.66% per annume, Meena invested at C.I. where as Tina invested at S.I. Meena gets rs 23 more money than what Tina got. How much money did each invest?

Answer 1

Let $P$ be the principal invested by Meena and Tina

Given Meena invests $CI$ and invested at $SI$ at $16.66\%$ Rate of interest for $2$ years.

$\therefore$ Let $A$ be the amount tina gets at the end of $2$ years

then Meena gets $A+23$

$A=P+\frac{P+R}{100}$

$A+23=P{(1+\frac{R}{100})}^T$

$P{(1+\frac{R}{100})}^2$

$P{(1+\frac{50}{3\times 100})}^2=P(1+\frac{2\times 50}{3\times 100})+23$

$P{(1+\frac{1}{6})}^2=P(1+\frac{1}{3})+23$

$P{\left(\frac{7}{6}\right)}^2=P\left(\frac{4}{3}\right)+23$

$\frac{49P}{36}-\frac{4P}{3}=23$

$\frac{49P-48P}{36}=23$

$P=23\times 36=828$ $\therefore$ The amount they invested is $828$ each