Question
Rs. 12000 is divided into two parts such that simple interest on the first part for 3 years at 12% per annum may be equal to the simple interest on the second part for $$4\frac{1}{2}$$ years at 16% per annum. The ratio of the first part to the second part is = ?
Answer: Option A
Let two parts are P1 and P2 respectively
According to the question
$$\eqalign{
& \frac{{{{\text{P}}_1} \times 3 \times 12}}{{100}} = \frac{{{{\text{P}}_2} \times 9 \times 16}}{{2 \times 100}} \cr
& 36{{\text{P}}_1} = 72{{\text{P}}_2} \cr
& \frac{{{{\text{P}}_1}}}{{{{\text{P}}_2}}} = \frac{{72}}{{36}} = \frac{2}{1} \cr
& {{\text{P}}_1}{\text{:}}{{\text{P}}_2} = 2:1 \cr
& {\text{Hence,}} \cr
& {\text{Required ratio = 2 : 1}} \cr} $$
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Let two parts are P1 and P2 respectively
According to the question
$$\eqalign{
& \frac{{{{\text{P}}_1} \times 3 \times 12}}{{100}} = \frac{{{{\text{P}}_2} \times 9 \times 16}}{{2 \times 100}} \cr
& 36{{\text{P}}_1} = 72{{\text{P}}_2} \cr
& \frac{{{{\text{P}}_1}}}{{{{\text{P}}_2}}} = \frac{{72}}{{36}} = \frac{2}{1} \cr
& {{\text{P}}_1}{\text{:}}{{\text{P}}_2} = 2:1 \cr
& {\text{Hence,}} \cr
& {\text{Required ratio = 2 : 1}} \cr} $$
Was this answer helpful ?
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