Question

A sum invested at $5\%$ simple interest per annum grows to $Rs.504$ in $4$ years. The same amount at $10\%$ simple interest per annum in $2\frac{1}{2}$ years will grow to:

• A. Rs 420
• B. Rs 450
• C. Rs 525
• D. Rs 550

Answer 1

The correct option is A Rs 420

For principal amount $x$

When $R=5\%,T=4$ years and Amount $\left(A\right)=Rs.504$

Therefore, SI $=504-x$

Hence, using, $SI=\frac{PRT}{100}$

$\Rightarrow 504-x=x\times \frac{5}{100}\times 4\Rightarrow 50400-100x=20x\Rightarrow 50400=120x\Rightarrow x=\frac{50400}{120}\Rightarrow x=Rs.420$

Now, $R=10\%,T=2\frac{1}{2}$ years and $P=Rs.420$

$\Rightarrow SI=\frac{420\times 10\times 5}{200}$

$=Rs.105$

Therefore, new amount $=420+105=Rs.525$