In this section we will solve difficult math problems with answers. You can work out the problems similiar to this and also check whether you are correct. The solutions to the problems are detailed and step by step.

## Difficult Math Problems With Answers

Following are few examples of solved problems.

Example 1: -

The average age of ten members in a family same as it was 4 years ago, because an old member has been replaced by a young member. Find how much younger is the new member?

Solution: -

Let the sum of the ages of nine member (total) be x

and the age of oldest member be z

so its average 4 yrs before = (x + z)/10.

After 4 years

let z be replaced by y.

Now each person’s age is increased by 4. So the new sum of ages of the nine members

= x + 4 x 10

= x + 40

So the new average age = (x + 40 + y )/10

Given that

now (x + z)/10=(x + 40 + y)/10

Multiplying by 10, we get (x + z) = x + 40 + y

Canceling x on both sides, we get

z = y + 40.

**So the older member is 40 years older than younger**

**Example 2 : -**

A computer can do "a" calculations in "b" seconds. Suppose we have to do c calculations. How many minutes will the computer take to complete the calculations?

**Solution: -**

Given that the computer can do "a" in "b" seconds . So in a second, it can do a/b calculations

In a minute, it can do 60a/b calculations

So a calculation require b/60a minutes

Given that it has to do c calculations

**So for c calculations, the computer will take cb/60a minutes**