Question

two natural numbers differ by 3 and their product is 180. find the numbers?

Answer 1

This is a difficult question, and there are two methods to get to the correct answer. I will show you the easier way, and you can contact me anytime if you need both the methods : )

This is the Hit and Trial method.

Two natural numbers differ by 3; the product is 180.

Let us take a natural number $x$

So, $x$ × ($x$ + 3) = 180

The last digit of the product is 0.
According to certain rules, when 2, 5 or 10 are multiplied, the last digits of their products can be 0. 

Now that we know what numbers we should use to get the answer, we can shrink down to smaller choices. 

Let's begin with 10 as $x$ (because it is the largest number among the three and will make it easier)
$x$ + 3 will be 13 

10 × 13 is 130
The numbers are not 10 and 13

Let's move on to the next numbers. We can't take 11 because we can only take a multiple of 2, 5 or 10.

The next possibility is 12.
When we take 12 as $x$, the other natural number becomes 15. ($x$ + 3)

12 × 15 is 180

And there is your answer. 12 and 15 are the two natural numbers.

Answer 2

Hey I have attached the solution. Please have a look. Hope it helps.... ^-^