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The ages of Pramod and Rohit are 16 years and 18 years respectively. In what ratio must they invest money at 5% p.a. compounded yearly so that both get the same sum on attaining the age of 25 years.

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400 : 441

250 : 350

300 : 301

500 : 552

answer is A.

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Detailed Solution

Time for which Pramod invests money = 25−16 = 9 years
Time for which Rohit invests money = 25−18 = 7 years
Pramod’s amount is calculated as:
⇒ A = P

{(1 + \frac{r}{100})}^{t}

⇒ A = PPramod

{(1 + \frac{5}{100})}^{9}

Rohit’s amount is calculated as:
⇒ A = P

{(1 + \frac{r}{100})}^{t}

⇒ A = PRohit

{(1 + \frac{5}{100})}^{7}

As Pramod and Rohit are to attain the same sum, therefore,
PPramod

{(1 + \frac{5}{100})}^{9} =

PRohit

{(1 + \frac{5}{100})}^{7}

Now, we need to find the ratio of principles of Pramod and Rohit.

\frac{P_{Pramod}}{P_{R o h it}}

\frac{{(1 + \frac{5}{100})}^{7}}{{(1 + \frac{5}{100})}^{9}}

\frac{1}{{(1 + \frac{5}{100})}^{2}}

\frac{1}{{(\frac{105}{100})}^{2}}

\frac{100}{105}

\frac{100}{105}

\frac{400}{441}

Therefore, the ratio in which Pramod and Rohit should invest money is 400 : 441.

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