Question

A number has two digit whose sum is 7 .if 27 is added to the number it digit get interchange. Find the number

Answer 1

Let us assume that one of the digit of the two digit number is X, then problem the other number will be (7 - X)

From problem we get that, if we add 27 to the number the digits get interchanged and also since the number is a two digit number then X will in tens place & (7 - X) will be in ones place.

So the equation we get

10X + (7 - X) + 27 = 10(7 - X) + X

10X + 7 - X + 27 = 70 -10X + X

9X + 34 = 70 - 9X

9X + 9X = 70 - 34

18X = 36

X = 36/18

X = 2,

So the digit in tens plsce = 2 & the digit in ones place is (7 - 2 = 5) 5, then the number is 25 and when 27 is added the result is 52, the digits interchange their position in the new number.

Ans: 25.

Answer 2

Hello !

Let the digit in unit's place be "y" and the digit in ten's place be "x"

Then the two digit no: is 10x + y

A.T.Q.,

x + y = 7 -----> (1)

also,

When digits are interchanged the no: is --> 10y +x

10x + y + 27 = 10y + x

10x - x + y - 10y = -27

9x - 9y = -27

9(x- y) = -27

x - y = -3 ----> (2)

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Adding (1) and (2) ,

x + y = 7

x - y = -3

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2x = 4

x = 2

x + y = 7

2 + y = 7

y = 7 -2

y = 5

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10x + y ---> 10(2) + 5 = 25

The no: is 25

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