Question

A sum of Rs.79,300 was divided into three parts such that their amounts after 2,3 and 4 years at 10% simple Interest were equal. The ratio between the three parts is -

• A. $91:84:78$
• B. $12:13:14$
• C. $\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$
• D. $\frac{1}{12}:\frac{1}{13}:\frac{1}{14}$

Answer 1

The correct option is A $91:84:78$

Let the three parts be $x,y,z$

$\therefore x+y+z=79,300⟶\left(I\right)$

Amount of $x$ after $2$ years

$=x(1+\frac{10\times 2}{100})$

$=\frac{6x}{5}$

Amount of ${}^{\prime }{y}^{\prime }$ after $3$ years

$=y(1+\frac{10\times 3}{100})$

$=\frac{13y}{10}$

ATP, $\frac{6x}{5}=\frac{13}{10}y$

$\Rightarrow x=\frac{13}{12}y\Rightarrow y=\frac{12}{13}x$

Amount of ${}^{\prime }{z}^{\prime }$ after $4$ years

$=z(1+\frac{10\times 4}{100})$

$=\frac{7z}{5}$

ATP, $\frac{6x}{5}=\frac{7}{5}z$

$\Rightarrow 6x=7z$

$\Rightarrow x=\frac{7}{6}z$

$\Rightarrow z=\frac{6x}{7}$

$x$ can be written as $\frac{91x}{91}$

$y=\frac{12x}{13}=\frac{12x\times 7}{13\times 7}=\frac{84x}{91}$

$z=\frac{6x}{7}=\frac{6\times 13x}{7\times 13}=\frac{78x}{91}$

$\therefore x:y:z=\frac{91x}{91}:\frac{84x}{91}:\frac{78x}{91}$

$=91:84:78$