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2 A two-digit number 'ab' can be represented as a sum of its respective place values i.e., ab = 10a + b Let's find the number by applying the given conditions in the question as follows Let the digits of the original number be x and y Hence, the original number is 10x + y (Assuming x to be the ten's digit and y to be the one's digit) After reversing the digits the new number will be 10y + x (After reversing, y becomes the ten's digit and x becomes the one's digit) According to the question, Condition 1: Sum of the original number and number obtained by reversing it = 165 Original number + New number = 165 By substituting the values we get, (10x+y)+(10y+x) = 165 ------------ (1) Condition 2: The digits of the original number differs by 3 x - y = 3 ---------------- (2) (since, it's given that ten's digit > one's digit) From equation (1) 11x + 11y = 165 Dividing by 11 on both the sides we get, x + y = 15 --------------- (3) By adding equation (2) and (3) we get, x - y + x + y = 3 + 15 ⇒ 2x = 18 ⇒ x = 9 ⇒ y = 15 - 9 = 6 Hence the original number is 10x + y = 10(9) + 6 = 96 Verification: We can verify the result by substituting the values in the given conditions: 96 + 69 = 165 9 - 6 = 3 Hence, both the conditions are satisfied. Thus, the required number satisfying the given conditions is 96 |
When you add two numbers and the number obtained by reversing the order of its digits is 165 if the both numbers differ by t hree find the number?
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