UPSC Civil Services 2017 Prelims General Studies Paper II

Let the two digit numbers are of the form ab.
So, 10a + b – (10b + a) = 27
⇒ 9a – 9b = 27
⇒ a – b = 3
(a, b) ⇒ (9, 6), (8, 5), (7, 4) (6, 3) (4,1), (5, 2)
Hence, 96 , 85 , 74 , 63 , 41, 52 and 25, 14, 36, 47, 58, 69 are the required numbers.