Question 2 - MCQs from NCERT Exemplar - Chapter 3 Class 10 Pair of Linear Equations in Two Variables

Transcript

Question 2 The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is (A) 25 (B) 72 (C) 63 (D) 36 Number is of the form Let Digit at Units place = y & Digit at Tens place = x Given that Sum of digits of two digit number is 9 ∴ Digit at tens place + Digit at units place = 9 x + y = 9 Also, If 27 is added to number, digits get reversed 27 + Number = Reversed number 27 + 10x + y = 10y + x 27 = 10y + x − 10x − y 27 = 9y − 9x 27 = 9(y − x) 27/9 = y − x 3 = y − x y – x = 3 Hence, our equations are x + y = 9 …(1) x – y = 3 …(2) Adding (1) and (2) (x + y) + (x − y) = 9 + 3 2y = 12 y = 12/2 y = 6 Putting y = 6 in (1) x + y = 9 x + 6 = 9 x = 9 – 6 x = 3 So, x = 3, y = 6 is the solution of our equation Therefore, Number = 10x + y = 10(3) + 6 = 30 + 6 = 36 So, the correct answer is (D)