Question

b. The digit at the tens place of a two-digit number is four times that is the units place. If the digits are
reversed, the new number will be 54 less than the original number. Find the number​

Answer 1

Answer:

Let the digit's in tens place be x

Let the digit's in tens place be xand digit in units place be y

Let the digit's in tens place be xand digit in units place be yHence the original number will be xy=10×x+y

Let the digit's in tens place be xand digit in units place be yHence the original number will be xy=10×x+yGiven that x=4y

Let the digit's in tens place be xand digit in units place be yHence the original number will be xy=10×x+yGiven that x=4yThen the reversed number will be yx=10×y+x

Let the digit's in tens place be xand digit in units place be yHence the original number will be xy=10×x+yGiven that x=4yThen the reversed number will be yx=10×y+xGiven: 

Let the digit's in tens place be xand digit in units place be yHence the original number will be xy=10×x+yGiven that x=4yThen the reversed number will be yx=10×y+xGiven:          yx=xy−27

Let the digit's in tens place be xand digit in units place be yHence the original number will be xy=10×x+yGiven that x=4yThen the reversed number will be yx=10×y+xGiven:          yx=xy−2710y+x=10x+y−27

Let the digit's in tens place be xand digit in units place be yHence the original number will be xy=10×x+yGiven that x=4yThen the reversed number will be yx=10×y+xGiven:          yx=xy−2710y+x=10x+y−27          9x=9y+27

Let the digit's in tens place be xand digit in units place be yHence the original number will be xy=10×x+yGiven that x=4yThen the reversed number will be yx=10×y+xGiven:          yx=xy−2710y+x=10x+y−27          9x=9y+27             x=y+3

Let the digit's in tens place be xand digit in units place be yHence the original number will be xy=10×x+yGiven that x=4yThen the reversed number will be yx=10×y+xGiven:          yx=xy−2710y+x=10x+y−27          9x=9y+27             x=y+3            4y=y+3      [ ∵ x=4y ]

Let the digit's in tens place be xand digit in units place be yHence the original number will be xy=10×x+yGiven that x=4yThen the reversed number will be yx=10×y+xGiven:          yx=xy−2710y+x=10x+y−27          9x=9y+27             x=y+3            4y=y+3      [ ∵ x=4y ]            3y=3

Let the digit's in tens place be xand digit in units place be yHence the original number will be xy=10×x+yGiven that x=4yThen the reversed number will be yx=10×y+xGiven:          yx=xy−2710y+x=10x+y−27          9x=9y+27             x=y+3            4y=y+3      [ ∵ x=4y ]            3y=3              y=1

Let the digit's in tens place be xand digit in units place be yHence the original number will be xy=10×x+yGiven that x=4yThen the reversed number will be yx=10×y+xGiven:          yx=xy−2710y+x=10x+y−27          9x=9y+27             x=y+3            4y=y+3      [ ∵ x=4y ]            3y=3              y=1and x=4(1)=4

Let the digit's in tens place be xand digit in units place be yHence the original number will be xy=10×x+yGiven that x=4yThen the reversed number will be yx=10×y+xGiven:          yx=xy−2710y+x=10x+y−27          9x=9y+27             x=y+3            4y=y+3      [ ∵ x=4y ]            3y=3              y=1and x=4(1)=4∴  The original number =41

Answer 2

Answer:

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Step-by-step explanation: