By interchanging the digits of a two digit number we get a number which is four times the original number minus 24. If the unit’s digit of the original number exceeds its ten’s digit by 7, then original number is?
বিকল্পসমূহ (নিজের উত্তর যাচাই করতে ক্লিক করুন):
সঠিক উত্তর
1 (29)
বিস্তারিত ব্যাখ্যা ও বিশ্লেষণ:
Solution:
Let, the two–digit number be = (10x + y) where x < y.
Number obtained on reversing the digits = (10y + x)
ATQ,
10y + x = 4 (10x + y) - 24
⇒ 40x + 4y - 10y - x = 24
⇒ 39x - 6y = 24
⇒ 13x - 2y = 8 ....(i)
Again, y - x = 7
y = x + 7 ....(ii)
⇒ 13x - 2 (x + 7) = 8
⇒ 13x - 2x - 14 = 8
⇒ 11x = 14 + 8 = 22
⇒ x = 22/11
∴ x = 2
From equation (ii),
y - 2 = 7
⇒ y = 2 + 7
∴ y = 9
So, Number = 10x + y = (10 × 2) + 9 = 29
