Question

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

• A. $12:13$
  
• B. $11:13$
  
• C. $16:15$
• D. $19:15$

Answer 1

The correct option is C $16:15$

Let the two parts be Rs $x$ and Rs $(1550-x)$ lent at $8\%$ and $5\%$ p.a.

Then, according to the question
$\Rightarrow \frac{x\times 8\times 3}{100}+\frac{(1550-x)\times 5\times 3}{100}=300$
$\Rightarrow 24x+1550\times 15-15x=30000$
$\Rightarrow 9x=30000-23250=6750$
$\Rightarrow x=\frac{6750}{9}=750$

Sum lent at $8\%=$ Rs. $750$

Sum lent at $5\%=1550-750=$ Rs. $800$
Required ratio = $800:750=16:15$