Question

A 3 digit number has all its digits even . The digit in its ones place is half of the digit in its tens place . The digit in its tens place is half of the digit in its hundreds place , then find the number?​

Answer 1

Step-by-step explanation:

Let a,b and c are the hundreds, tens and units places digits respectively. then digit =100a+10b+c

Interchanging units and tens places digits, we get

⇒100a+10c+b=100a+10b+c+36

⇒c−b=4…eqn(1)

Now, Interchanging units and hundreds places digits, we get

⇒100c+10b+a=100a+10b+c−198

⇒a−c=12…eqn(2)

From equation 1 and 2,

a−b=6…eqn(3)

Suppose number is increased by x, If we change tens and hundreds digits,

⇒100b+10a+c=100a+10b+c+x

⇒−x=90a−90b

⇒x=−540

Thus, number is decreased by 540.