Question

A sum was put at simple interest at a certain rate for $4$ years. Had it been put at $2$% higher rate, it would have fetched Rs $112$ more. Find the sum.

• A. $1400$
• B. $1200$
• C. $1000$
• D. $1600$

Answer 1

The correct option is A $1400$

$(SI{)}_1=\frac{P\times r_1\times t}{100}$

$(SI{)}_2=\frac{P\times r_2\times t}{100}$

$r_2=r_1+2$

$(SI{)}_2=(SI{)}_1+112$

$t=4$

$⟹(SI{)}_1+112=\frac{P\times r_2\times t}{100}$

$⟹\frac{P\times r_1\times t}{100}+112=$$\frac{P\times r_2\times t}{100}$

$⟹\frac{P\times r_1\times t}{100}-$$\frac{P\times r_2\times t}{100}=112$

$⟹\left(4P/100\right)(r_2-r_1)=112$

$⟹P\times 4\times 2=112\times 100=Rs.1400$