Question

The digit at the tens's place of two digit number is four times that in the unit's place.If the digits are reversed,the new number will be 54 less than the original number.Find the original number​

Answer 1

Answer:

Let us take the digit at the ten's place as X and digit at one's place as Y.

given: x = 4y

original number= 10x+y or 41y (x=4y)

reversed number = (10y +x)  or 14 y

as 10y +x is 54 less than 10x+y, we can say

41y - 14y = 54

27y = 54

therefore, y = 54/27

                    = 2

therfore, y = 2

since x = 4y, x=8

therefore the original number is 82 and the reverse is 28.

we can check the solution by subtracting the two:

82-28 = 54

as the condition holds, answer is verified.

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Answer 2

Step-by-step explanation:

Let the Number at the units place be x.Tenth place = 4x

Then,

➳ Number = 10(x) + 4x

➳ Number = 10x + 4x

➳ Number = 14x

______________________

➳ Reversing Number = 10(4x) + x

➳ Reversing Number = 40x + x

➳ Reversing Number = 41x

According to Question now,

➳ 14x - 41x = -54

➳ -27x = -54

➳ x = -54/-27

➳ x = 54/27

➳ x = 2

Units place = x = 2

Tenths place = 4x = 4(2) = 8

Therefore,

Number = 10(8) + 2 = 80 + 2 = 82