Sudhir had Rs 45,000. He lent a part of it at 4% p.a. and the remaining at 10% p.a. simple interest. He earned a total profit at 8% p.a. on the money lent, what sum did he lend at 10% p.a. ?

Rs 30,000

$\text{Total money}=45000.$

$\text{Overall rate}=8\%.$

$\text{Rates}=4\%,\;10\%.$

$\text{By alligation:}$

$4\% \;\;\;\;\;\;\;\; 10\%$

$\;\;\;\;\;\;8\%$

$10-8=2,\;\;8-4=4.$

$\text{Ratio at }4\%:10\% = 2:4 = 1:2.$

$\text{Money at }10\%=\frac{2}{3}\times45000=30000.$

$\text{Sum lent at }10\% = ₹30,000.$