A man invests Rs. $5000$, partly at $5\%$ and partly at $6\%$, total interest in $1$ year being Rs. $280$.…

A man invests Rs. $5000$, partly at $5\%$ and partly at $6\%$, total interest in $1$ year being Rs. $280$. Amount at $5\%$ is
  1. Rs. $2000$
  2. Rs. $3000$
  3. Rs. $1000$
  4. Rs. $4000$

Solution

$x + y = 5000$ and $\dfrac{5x}{100} + \dfrac{6y}{100} = 280 \Rightarrow 5x + 6y = 28000$. Multiply first by 5: $5x + 5y = 25000$. Subtract: $y = 3000$, so $x = 2000$.

Asked in: MH-SSC-9

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