Question

A man invests a certain sum of money at $6\%p.a.$ simple interest and another sum at $7\%p.a.$ simple interest. His income from interest after $2$ years was $Rs.354$. One-fourth of the first sum is equal to one-fifth of the second sum. The total sum invested was

• A. $Rs.1500$
• B. $Rs.1200$
• C. $Rs.2700$
• D. $Rs.5400$

Answer 1

The correct option is C $Rs.2700$

Let the sum be $x$ and $y.$

then according to the question

$\Rightarrow \frac{x\times 6\times 2}{100}+y\times 7\times 2/100=354$

$\Rightarrow 12x+14y=35400$

$\Rightarrow 6x+7y=\mathrm{17700.....................}eq1$

One-fourth of the first sum is equal to one-fifth of the second sum

Then $\frac{x}{4}=\frac{y}{5}$

$\Rightarrow 5x=4y$

$\Rightarrow 5x-4y=\mathrm{0...........}eq2$

Multiply eq 1 by 4

$\Rightarrow 24x+28y=\mathrm{70800.............}eq3$

Multiply eq 2 by 7

$\Rightarrow 53x-28y=\mathrm{0.................}eq4$

Add eq 3 and eq4

$\Rightarrow 59x=70800$

$\Rightarrow x=1200$

Put the value of $x$ In eq2

$\Rightarrow 5\times 1200-4y=0$

$\Rightarrow -4y=-6000$

$\Rightarrow y=1500$

$Totalsum=1200+1500=2700Rs.$