Question

I am 3 digit number,i am a even number,sum of my digit is a prime number,four timrs of my tens digit is equal to three times ones digit,my hundred digit is the largest digit,my ones digit is ones less the hundred s digit i am?

Answer 1

Answer:

Suppose the number be XYZ

Then , its general form is 100x + 10y + z

Now , according to question ,

4y = 3z ( Given)

hence , z = ( 4/3 ) × Y

Now , x = Y + 1 ( Given )

Hence , we conclude that ,

The number is

Y + 1 Y ( 4/3) × Y -( as we writtten in first line the number to be XYZ , similarily , we can write XYZ like this)

Now , focus on one's digit ,

The number seems to be fractional or say decimal ,

To get number as integers ,we should take value of 'Y' as a multiple of 3 so that it can he divided by denominator of 4 / 3.

Hence , Case 1 -

when Y = 3

Then , x = Y +1 = 4

and z = 4 .

Hence , The number is 434.

Case 2-

when Y = 6 ,

then , X = 7 and Z = ( 4 / 3 ) × 6 = 8.

Hence , number is 768.

From cases (1) and (2) , possible numbers are ,

768 and 434. But according to question , sum of digits should be prime number , but the number obtained from adding digits of number obtained in Case ( 2 ) is a composite number . --------( 7 + 6 + 8 = 21 and 21 is composite)

Hence , the number must be 434 as sum of its digits is 11 which is prime.

Hence , the number is 434.

This was an easy question but it takes much time to explain by writting and texting ....kindly thanks and follow for my hardwork as i am lazy.