Question 31

A two digit number is 7 times the sum of its two digits. The number that is formed by reversing its digits is 18 less than the original number. What is the number?

Solution

Let the two-digit number be "ab". This can be represented as 10a + b

A two-digit number is 7 times the sum of its two digits.

10a + b = 7a + 7b

a = 2b

Number formed by reversing the digits = "ba" = 10b + a

The reversed number is 18 less than the original number.

10b + a = 10a + b -18

9a - 9b = 18

9(2b) - 9b = 18

b = 2

Thus, a = 2b = 4

Thus, the two-digit number is 42.

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