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A two digit number is such that the product of its digits is 18.When 63 is subtracted from the number, the digits interchange their places. Find the number |
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Answer» duct of the DIGITS of a two digit NUMBER is 18.When 63 is subtracted from the original number, the digits interchange their places.What is the original number ?Let the digit at TEN's place be 'x' and the digit at the unit's place be 'y'CASE:- 1)✧ The product of the digits of a two digit number is 18➠ xy = 18...❶CASE:- 2)✧ When 63 is subtracted from the original number, the digits interchange their places❮ Reversed Number = 10y + x ❯➠ 10x + y –63 = 10y + x➠ 10x + y –10y –x = 63➠ 9X –9y = 63Take common '9' from both sides➠ x –y = 7➠ x = 7 + y...❷Put the value of 'x' from EQUATION 2) in equation 1)➠ (7 + y)y = 18➠ 7y + y² = 18➠ y² +7y –18 = 0➠ y² +(9 –2)y –18 = 0➠ y² +9y –2y –18 = 0➠ y(y +9) –2(y +9) = 0➠ (y –2) (y +9) = 0Put the value of 'y' in equation 2), we get➠ x = 7 + 2❒ NUMBER = 10x + y❒ NUMBER = 10(9) + 2❝ Hence, the number formed is 92 ❞______________________ |
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