HOW TO SOLVE PROBLEMS ON NUMBERS 

Problem:

If a number when divided by 296 gives a remainder 75, find the remainder when 37 divides the same number.

Solution:

Step 1 :

Let us understand the given information. There is only one  information given in the question. 

When a number is divided by 296 gives a remainder 75.

Step 2 :

Target of the question: Find the remainder when 37 divides the same number.

Step 3 :

Let "x" be the given number.

We have to find the remainder, when "x" is divided by 37. 

(Do remember, our aim is not to get the value of "x")

Step 4 :

When "x" is divided by 296, the remainder is 75.   

Let "k" be the quotient when "x" is divided by 296.

Then, we have

x  =  296k + 75

In the above equation, "296" is divisor and  "75" is remainder.

Step 5 :

We want to find the remainder when we divide the same number "x" by 37.  To do this, we need to have 37 at the place where we have "296"  in the above equation.

So we can write 296 as 37 times 8 and 75 as 37 times 2 plus 1.

It is shown below.

x  =  296k + 75

x  =  (37x8)k + (37x2 + 1)

x  =  37x8k + 37x2 + 1

x  =  37(8k+2) + 1

Step 6 :

Clearly, the above equation says that when the number "x" is divided by 37, the remainder is "1".

Therefore, when 37 divides the given number, remainder is "1".

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