A man invested a sum of N280.00 partly at 5% and partly at 4%. if the total interest is N12.80 per annum, find the amount invested at 5%
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Correct Answer: Option D
Explanation:
Let the amounts invested at 4% and 5% respectively be x and y.
\(\therefore x + y = 280 ... (i)\)
Interest on x = \(\frac{x \times 4 \times 1}{100} = 0.04x\)
Interest on y = \(\frac{y \times 5 \times 1}{100} = 0.05y\)
\(\therefore 0.04x + 0.05y = 12.80\)
\(\implies 4x + 5y = 1280 ... (ii)\)
From (i), \(x = 280 - y\).
Put into (ii), \(4(280 - y) + 5y = 1280\)
\(1120 - 4y + 5y = 1280\)
\(1120 + y = 1280 \implies y = 1280 - 1120 = N160\)
\(\therefore\) N160 was invested at the rate of 5% per annum.
Let the amounts invested at 4% and 5% respectively be x and y.
\(\therefore x + y = 280 ... (i)\)
Interest on x = \(\frac{x \times 4 \times 1}{100} = 0.04x\)
Interest on y = \(\frac{y \times 5 \times 1}{100} = 0.05y\)
\(\therefore 0.04x + 0.05y = 12.80\)
\(\implies 4x + 5y = 1280 ... (ii)\)
From (i), \(x = 280 - y\).
Put into (ii), \(4(280 - y) + 5y = 1280\)
\(1120 - 4y + 5y = 1280\)
\(1120 + y = 1280 \implies y = 1280 - 1120 = N160\)
\(\therefore\) N160 was invested at the rate of 5% per annum.