In a two-digit number, tens digit is a multiple of the units digit. The sum of the number and the number formed by reversing the digits is 132. Which of the folloiwng can be the product of the two digits ?

Options

A. 16
B. 27
C. 35
D. 18

Answer

b

Explanation

Let the units digit of the number be x and the ten's digit be `nx` and the number formed is `10 xx nx`
`+x` and the number by reversing the digits is `10 x + nx`.
Given that `10 nx + x + 10 x + nx = 132`
`11nx + 11x = 132`
`11(nx + x) = 132`
`:.` Sum of the digits = 12
This is possible with the digits `9, 3 or 8,4 or 6,6`
`{:("Sum of the Number","Product of the Digits"),(93 + 39 = 132,27),(84 + 48 = 132,32),(66 + 66 = 132,36):}`
Hence, the correct option is (b)