A man invested an amount at 12% per annum simple interest and another amount at 10% per annum simple interest. He received an annual interest of Rs.1145. But, if he had interchanged the amounts invested, he would have received Rs.90 less. What amounts did he invest at the different rates?

Step-by-step explanation:

Let we assume that

Sum invested at the rate of 12 % per annum be Rs x

Sum invested at the rate of 10 % per annum be Rs y

According to statement,

Annual interest earned = Rs 1145

We know,

Interest received on a sum of Rs p invested at the rate of r % per annum for n years is

So, we get

According to second condition

Sum invested at the rate of 12 % per annum be Rs y

Sum invested at the rate of 10 % per annum be Rs x

According to statement,

Annual interest earned = Rs 1055

So,

Now, On adding equation (1) and (2), we get

On Subtracting equation (2) from equation (1), we get

On adding equation (3) and (4), we get

On substituting the value of x in equation (3), we get

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

So,

Sum invested at the rate of 12 % per annum be Rs 7250

Sum invested at the rate of 10 % per annum be Rs 2750

answer:   35 % is the probability of a late departure or an early arrival.

step-by-step explanation:

let l represents the late departure and e represents the early departure.

then, according to the question,

p(l) = 12 %,   p(e) = 27 % and = 4 %

and, we have to find out,

but, we know that,

which is the required equation that will use to find the probability of a late departure or an early departure.

therefore,   the probability of a late departure or an early arrival =   35 %