Question

26. If I reverse the digits of a two-digit positiveinteger and subtract the resulting integer fromthe original integer, the difference is 36. Thedifference between the two digits isA) 4 B) 6 C) 8 D) 9

Answer 1

Represent the two digits using x and y. The digit number is xy and the reverse is yx

From the first statement, we can deduce mathematically that

`\begin{gathered} xy-yx=36 \\ (10x+y)-(10y+x)=36 \end{gathered}`
`\begin{gathered} 10x+y-10y-x=36 \\ 10x-x+y-10y=36 \\ 9x-9y=36 \\ x-y=4-----\text{eqn}(1) \end{gathered}`

From the second statement, we can deduce mathematically that

`x-y=\text{?}----\text{eqn}(2)`

Comparing equation (1) and equation (2)

`\begin{gathered} \text{equation (1) is equal to equation (2)} \\ \text{Therefore for equation 2, } \\ x-y=4 \end{gathered}`

Hence, the difference between the two digits is 4, OPTION A