1.

The hundreds digit of a three-digit number is 7 more than the units digit. The digit of the number are reversed, and the resulting number is subtracted from the original three-digit number. The units digit of the final number so obtained is

Answer» Correct Answer - Option 4 : 3

Given:

The hundreds digit of a three-digit number = 7 + units digit.

Concept:

Place value: The digit of any number is called its place value.

For example, in the number 256, the place value of 5 is 5.

Face value: It is the actual value of any digit in a particular number.

For example, in the number 256, the face value of 5 is 50.

Any number can be written as the sum of, a product of the face value and place value.

for three digit number, 

abc = 100a + 10b + c

Calculation:

Let the three-digit number is 'abc'

according to question,

a = 7 + c    

⇒ a - c = 7       .......(1)

Now, according to above discussion 'abc' can be written as,

abc = 100a + 10b + c    ......(2)

on reversing the number, we get the new number 'cba'

⇒ cba = 100c + 10b + a      ......(3)

Substracting equation (2) from (1)

abc - cba = ( 100a + 10b + c ) - ( 100c + 10b + a ) 

abc - cba = 99( a - c )

abc - cba = 99 × 7 = 693     [ from equation (1) ]

Hence, unit digit of final number will be 3.


Discussion

No Comment Found

Related InterviewSolutions