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One of the two digits of a two digit number is three times the other digit. If you interchange the digit of this two-digit number and add the resulting number to the original number, you get 88. What is the original number?

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Engineering graduate from NIT Calicut, Rank holder (#47) in State Entrance Examination.

Assume the 2 digit number as xy, where x and y are first and second digits respectively. x=3y..............(1) new number after interchanging digits is yx. xy+yx=88 that means 10x+y+10y+x=88 11x+11y=88 11(x+y)=88 x+y=88/11=8..............(2) substituting (1) in (2) 3y+y=8 4y=8 y=8/4 y=2 x=3y=3*2=6 original...
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Assume the 2 digit number as xy, where x and y are first and second digits respectively. 

x=3y..............(1)

new number after interchanging digits is yx.

xy+yx=88

that means

10x+y+10y+x=88

11x+11y=88

11(x+y)=88

x+y=88/11=8..............(2)

substituting (1) in (2) 

3y+y=8

4y=8

y=8/4

y=2

x=3y=3*2=6

original number=xy=62

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Let the digits at tens place and ones place be x and 3x respectively. Therefore, original number = 10x + 3x = 13x On interchanging the digits, the digits at ones place and tens place will be x and 3x respectively. Number after interchanging = 10 × 3x + x = 30x + x = 31x According to the given...
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Let the digits at tens place and ones place be x and 3x respectively.

Therefore, original number = 10x + 3x = 13x

On interchanging the digits, the digits at ones place and tens place will be x and 3x respectively.

Number after interchanging = 10 × 3x + x = 30x + x = 31x

According to the given question,

Original number + New number = 88

13x + 31x = 88

44x = 88

Dividing both sides by 44, we obtain

x = 2

Therefore, original number = 13x = 13 × 2 = 26

By considering the tens place and ones place as 3x and x respectively, the two-digit number obtained is 62.

Therefore, the two-digit number may be 26 or 62.

 

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