₹10,000 is lent, part at 8% and the rest at 12% simple interest a year. The total interest for one year is ₹1,040. How much is lent at 8%?

Explanation

1. 01

   The mean rate is $\frac{1{,}040}{10{,}000} = 10.4\%$. Alligation: $(12 - 10.4) : (10.4 - 8) = 1.6 : 2.4 = 2 : 3$.

2. 02

   At 8%: $\frac{2}{5} \times 10{,}000 = 4{,}000$ rupees.