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Previous Year Question (PYQs)

When you reverse the digits of the number 13, the number increases by 18. How many other two digit numbers increase by 18 when their digits are reversed?




Solution

Let the two-digit number be $10a + b$. Reversed number $= 10b + a$. Given increase is $18$: $(10b + a) - (10a + b) = 18$ $9(b - a) = 18$ $b - a = 2$ Possible digit pairs $(a,b)$ are: $(1,3), (2,4), (3,5), (4,6), (5,7), (6,8), (7,9)$ Total such numbers $= 7$.

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