Question

Use matrix multiplication to divide rs. 30,000 in two parts such that the total annual interest at 9% on the first part and 11% on the second part amounts rs. 3060.

Answer 1

Given :

Total principal amount  = Rs 30,000

Annual interest rate for first part = 9 %

Annual interest rate for second part = 11%

The sum of interest = Rs 3060

To Find :

The Principal divided for each rate of interest

Solution :

Let The principal amount for 9% rate = Rs p

And The principal amount for 11% rate = Rs ( 30,000 - p )

From Simple Interest method

Simple Interest = $\dfrac{principal\times rate\times time}{100}$

At interest rate 9%

S.I = $\dfrac{p\times 9\times 1}{100}$

At interest rate 11%

s.i = $\dfrac{(30,000-p)\times 11\times 1}{100}$

∵  The sum of interest = Rs 3060

i.e  S.I + s.i =  3060

Or,    $\dfrac{p\times 9\times 1}{100}$   +  $\dfrac{(30,000-p)\times 11\times 1}{100}$  = 3060

Or,   9 p + ( 330000 - 11 p ) = 3060 × 100

or,    9 p - 11 p + 330000 = 306000

Or,   11 p - 9 p = 330000 - 306000

Or,            2 p = 24,000

∴                  p = $\dfrac{24,000}{2}$

i.e                 p = Rs 12,000

So, The principal amount for 9% rate = p = Rs 12,000

Now,

The principal amount for 11% rate = Rs ( 30,000 - 12,000 ) = Rs 18,000

Hence, The  principal amount for 9% rate of interest is Rs 12,000

And The principal amount for 11% rate is Rs 18,000  . Answer