CAT 2020 Set-1 | Question: 52

Question

Veeru invested Rs $10000$ at $5\%$ simple annual interest, and exactly after two years, Joy invested Rs $8000$ at $10\%$ simple annual interest. How many years after Veeru’s investment, will their balances, i.e., principal plus accumulated interest, be equal?

Answer 1

Given that,

Veeru$:$

• Principle $(P_{1}) = \text{Rs} \; 10000$
• Rate $(R_{1}) = 5 \%$

Joy$:$

• Principle $(P_{2}) = \text{Rs} \; 8000$
• Rate $(R_{2}) = 10 \%$

Let the time after Joy’s investment, when the balances become equal be $n$ years. i.e., principal plus accumulated interest. 

$ P_{1} + \left[ \dfrac{P_{1} \times R_{1} \times (n+2)}{100} \right] = P_{2} + \left[ \dfrac{P_{2} \times R_{2} \times (n)}{100} \right] $

$ \Rightarrow 10000 + \left[ \dfrac {10000 \times 5 \times (n+2)}{100} \right] = 8000 + \left[ \dfrac{ 8000 \times 10 \times (n)}{100} \right] $

$ \Rightarrow 2000 + 500 (n+2) = 800n $

$ \Rightarrow 2000 + 500n + 1000 = 800n $

$ \Rightarrow 3000 = 300n $

$ \Rightarrow \boxed {n = 10 \; \text{years}}$

Since, Veeru’s investment was made $(n+2) \; \text{years}$ ago.

$\therefore$ The balance will be equal after Veeru’s investment, after $12 \; \text{years.}$

Correct Answer $: 12$