A two-digit number becomes five-sixth of itself when its digits are reversed . The two digits differ by one. What is the number ?

A two-digit number becomes five-sixth of itself when its digits are reversed . The two digits differ by one. What is the number ? Correct Answer 54

ধরি, একক স্থানীয় অংক = x দশক ,, ,, = y ∴ সংখ্যাটি = 10 y + x প্রশ্নমতে, 56(10  y  + x)  = 10x  + y ⇒ 50y  +  5x  = 60x  +  6y ⇒44y  = 55x ⇒ y  =   5544x ........ .. (i)  আবার, y – x = 1 ⇒ 5544 x – x = 1 [ (i) নং হতে] ⇒55x  -  44x44 = 1 ⇒11x = 44 ⇒ x = 4 ∴ y – 4 = 1 ⇒ y 5 ∴ সংখ্যাটি হলো : 54।
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