A money lender lends Rs. 400 for 3 years to a person and lends Rs. 500 for 4 years to the other person at the same rate of simple interest. If altogether he receives Rs. 160 as interest, what is the rate of interest per annum ?

Let the rate of interest = $$r\%$$

For the first person, Principal $$(P_1)=Rs. 400$$ and time $$(T_1)=3$$ years

For the second person, Principal $$(P_2)=Rs. 500$$ and time $$(T_2)=4$$ years

Total interest earned under simple interest = Rs. 160

=> $$(\frac{P_1 \times r \times T_1}{100})+(\frac{P_2 \times r \times T_2}{100})=160$$

=> $$(\frac{400 \times r \times 3}{100})+(\frac{500 \times r \times 4}{100})=160$$

=> $$12r+20r=160$$

=> $$32r=160$$

=> $$r=\frac{160}{32}=5\%$$

=> Ans - (A)