Question

Divide by 9, I leave a remainder of 6. Divided by 4, I leave a remainder of 1. Divided by 10 , I leave a remainder of 3. Who am I?

Answer 1

Answer:-

Divide by 9 , I leave a remainder of 6 :-

I am 15.

Divided by 4, I leave a remainder of 1 :-

I am 5.

Divided by 10 , I leave a remainder of 3:-

I am 13.

Answer 2

Given:

On division by 9, number gives = 6

On division by 4 number gives = 1

On division by 10 number gives = 3

To Find:

The number

Solution:

Let the number be = x.

Therefore, according to the question -

First equation -  

x/9 = P + 6/9, or

x = 9P + 6 --- 1

Second equation -  

x/4 = Q + 1/4, or

x = 4Q + 1 --- 2

Third equation -  

x/10 = R + 3/10, or

x = 10R + 3 --- 3  

From (1) and (2):

9P + 6 = 4Q + 1, or

4Q = 9P + 5 --- 4  

From (2) and (3):

4Q + 1 = 10R + 3, or

4Q = 10R + 2 --- 5  

From (4) and (5):

9P + 5 = 10R + 2, or

9P = 10R - 3 --- 6  

Now, In sixth equation if R = 3, then

9P = 30–3

9P= 27

P = 3.

From fifth equation - 4Q = 10R + 2. If R = 3, then

4Q = 30+2

4Q = 32

Q = 4.

So, on solving x = 33.

Answer: The number is 33