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The sum of the digits of a two-digit number is 15. On subtracting 27 from the given number its digits get reversed. Find the given number. |
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Answer» Answer: The required two-digit NUMBER is 96. Step-by-step-explanation: Let the digit at the TENS place be x. And the digit at the units place be y. ∴ The original number = 10X + y And the number obtained by interchanging the digits = 10y + x From the first condition, x + y = 15 ⇒ x = 15 - y ⇒ x = - y + 15 - - ( 1 ) From the second condition, 10x + y - 27 = 10y + x ⇒ 10x + y - 10y - x = 27 ⇒ 9x - 9y = 27 ⇒ x - y = 3 - - [ Dividing both sides by 9 ] ⇒ ( - y + 15 ) - y = 3 - - - [ From ( 1 ) ] ⇒ - y + 15 - y = 3 ⇒ - y - y = 3 - 15 ⇒ - 2y = - 12 ⇒ 2y = 12 ⇒ y = 12 ÷ 2 ⇒ y = 6 By substituting y = 6 in equation ( 1 ), we get, x = - y + 15 - - ( 1 ) ⇒ x = - 6 + 15 ⇒ x = 9 Now, The original number = 10x + y ⇒ The original number = 10 × 9 + 6 ⇒ The original number = 90 + 6 ∴ The original number = 96 The required two-digit number is 96. |
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