Q1 of 55 Page 72

The units digit of a two-digit number is 3 and seven times the sum of the digits is the number itself. Find the number.

It is given that the units place digit is 3.


So, let tens place digit be y.


∴ Our number = (10y + 3) …(1)


Our given condition is that seven times the sum of the digits is the number itself.


∴ By given condition,


7(y + 3) = (10 y + 3)
7 y + 21 = 10 y + 3
∴ 10 y - 7y = 21 - 3
∴ 3 y = 18
∴ y = 6


Substituting the value of y in equation1,


Number = 10 × 6 + 3 = 63


Hence, required number is 63.


More from this chapter

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2

In a two-digit number, the digit at the unit place is double the digit in the tens place. The number exceeds the sum of its digits by 18. Find the number.

 3

A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, its digits are reversed. Find the number.

 4

The sum of the digits of a two-digit number is 15. The number obtained by interchanging its digits exceeds the given number by 9. Find the original number.

 5

The difference between a 2-digit number and the number obtained by interchanging its digits is 63. What is the difference between the digits of the number?