Question

The units digit of a number is 3. The number is seven times the sum of its digits. Find the number

Answer 1

Sol:
Units digit of a two digit number = 3
Let the tens digit of the number be x.
Number = 10x + 3
Sum of the digits = (x + 3)

Given that 7 times the sum of the digits is the number itself.

⇒ 7(x + 3) = (10x + 3)

⇒ 7x + 21 = 10x + 3

⇒ 10x - 7x = 21 - 3

⇒ 3x = 18

⇒ x = 6.

Therefore, the digits in the tens place is 6 and the number is 63.

Answer 2

Let x be in the ten's place and y be in unit's place. Then the number thus formed is : 10x + y
But it is given that y = 3. Thus the number is 10x + 3
=> 10x + 3 = 7(x + y) => 10x + 3 = 7x + 7y
=> 10x - 7x = 7(3) - 3 = 21 - 3 = 18
=> 3x = 18 => x = 18/3 = 6
and given that y = 3.
Thus the number formed is 63.