Question
A man invests half of his capital at the rate of 10% per annum, one - third at 9% and the rest at 12% per annum. The average rate of interest per annum, which he gets is = ?
Answer: Option B
Let the total amount = Rs. 6
Total average rate of interest
$$\eqalign{
& {\text{ = }}\frac{{\left( {3 \times 10\% } \right) + \left( {2 \times 9\% } \right) + \left( {1 \times 12\% } \right)}}{6} \cr
& = \frac{{\left( {30 + 18 + 12} \right)}}{6} \% \cr
& = 10\% \cr} $$
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Let the total amount = Rs. 6
Total average rate of interest
$$\eqalign{
& {\text{ = }}\frac{{\left( {3 \times 10\% } \right) + \left( {2 \times 9\% } \right) + \left( {1 \times 12\% } \right)}}{6} \cr
& = \frac{{\left( {30 + 18 + 12} \right)}}{6} \% \cr
& = 10\% \cr} $$
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