A man has Rs 50,000.He invests some part of it in one bank @ of 11 p.c.p.a. and the remaining money in another bank @ of 9 p.c.p.a.He gets a combined simple interest of Rs 5,400(i.e the S.I of one bank + S.I of another bank = 5,400).Then find the amount of money invested in both the banks individually
.11 a + .09 b = 5400
but
b = 50,000 - a
so
.11 a + .09 (50,000 -a) = 5400
.11 a + 4500 - .09 a = 5400
.02 a = 900
a = 45,000
then
b = 5,000
To find the amount of money invested in both the banks individually, we can use the following steps:
Let's assume the amount invested in the first bank (at 11% per annum) is x.
So, the amount invested in the second bank (at 9% per annum) will be Rs 50,000 - x.
We know that the formula for calculating simple interest is S.I. = (Principal * Rate * Time) / 100.
Now, let's calculate the simple interest of the amount invested in the first bank.
S.I.1 = (x * 11 * 1) / 100
And the simple interest of the amount invested in the second bank.
S.I.2 = ((50,000 - x) * 9 * 1) / 100
According to the given conditions, the sum of the two simple interests is Rs 5,400.
So, S.I.1 + S.I.2 = 5,400
((x * 11 * 1) / 100) + (((50,000 - x) * 9 * 1) / 100) = 5,400
Now, we can solve the above equation to find the value of x. Let's do it step by step.
(11x / 100) + ((450,000 - 9x) / 100) = 5,400
11x + 450,000 - 9x = 5,40000
2x + 450,000 = 5,40000
2x = 5,40000 - 450,000
2x = 100,000
x = 100,000/2
x = 50,000
Therefore, the amount invested in the first bank is Rs 50,000.
And the amount invested in the second bank is Rs 50,000 - Rs 50,000 = Rs 0.
So, the man has invested Rs 50,000 in the first bank and Rs 0 in the second bank.