Question

Divide Rs 2000 into two sums such that, if the first be put out at simple interest for 6 years at $3\frac{1}{2}$ per cent and the second for 3 years at $4\frac{1}{2}$ per cent, the interest on the first sum shall be double that of the second.

• A. Rs 725 Rs 1275
• B. Rs 1125, Rs 875
• C. Rs 1500, Rs 500
• D. Rs 635, Rs 1365

Answer 1

Answer: (B)

Rs 1125, Rs 875

Let us divide $Rs2000$ into two parts,

the first part is $x$ & the second part is $2000-x$.

In the first case, the Principal $P=x$, Rate $R=3\frac{1}{2}p.c=\frac{7}{2}p.c,$ & Time $T=6$yrs.

Let the interest on Rs x =$I_x$.

$\therefore I_x=\frac{PRT}{100}=\frac{x\times \frac{7}{2}\times 6}{100}=\frac{21x}{100}.$

In the second case,

the Principal $P=2000-x$, Rate R=$4\frac{1}{2}p.c=\frac{9}{2}p.c,$ & Time $T=3$yrs.

Let the interest on Rs(2000-x) =$I_{2000-x}$.

$\therefore I_{2000-x}=\frac{PRT}{100}=\frac{2000-x\times \frac{9}{2}\times 3}{100}=\frac{54000-27x}{200}.$

So, by the given condition,

$\therefore I_x=2\times I_{2000-x}⟹\frac{21x}{100}=2\times \frac{54000-27x}{200}⟹48x=54000⟹x=Rs1125.\therefore 2000-x=Rs(2000-1125)=Rs875.$

So the required amounts are $Rs1125$ & $Rs875$.

Ans- Option B.