NCERT Class 12 Maths · Chapter 3 Matrices · Exercise 3.2 Question 19

✅ Step-by-Step Solution

1. Let X,Y be the amounts invested at 5% and 7%. The matrix equation is \(\left[\begin{matrix}1 & 1\\\frac{1}{20} & \frac{7}{100}\end{matrix}\right]\)\(\left[\begin{matrix}x\\y\end{matrix}\right]\) = \(\left[\begin{matrix}30000\\t\end{matrix}\right]\).
2. For interest ₹1800, subtract 0.05(X+Y)=1500 from 0.05X+0.07Y=1800 to get 0.02Y=300. Thus X = \(15000\), Y = \(15000\).
3. For interest ₹2000, subtract 0.05(X+Y)=1500 from 0.05X+0.07Y=2000 to get 0.02Y=500. Thus X = \(5000\), Y = \(25000\).
4. Both allocations are nonnegative and sum to ₹30000; substituting gives the stipulated annual interest.