₹5,000 is divided into two parts such that if one part is invested at 4% and the other at 5%, then the whole annual interest from both the sums is ₹223. How much was invested at 4% ?

₹2,700

Total principal (P)  =5000

Let P₁ = X                 i.e. invested at 4% and

P₂ = 5000 - X            i.e. invested at 5%

Interest = I and Time = T

ATQ

⇒ I₁ + I₂= 223

⇒ \(\frac{P_1\;×\;R_1\;×\;T_1}{100}\) + \(\frac{P_2\;×\;R_2\;×\;T_2}{100}\) = 223

⇒ \(\frac{X\;×\;4\;×\;1}{100}\) + \(\frac{(5000-X)\;×\;5\;×\;1}{100}\) = 223

⇒ \(\frac{4X}{100}\) + \(\frac{25000}{100}\) - \(\frac{5X}{100}\) = 223

⇒ \(\frac{X}{100}\) = 250 - 223

⇒ \(\frac{X}{100}\) = 27

⇒ X = 2700