Question

A number consists of two digits whose sum is 7.if 27 is added to the number,the digits are reversed.find the no

Answer 1

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
--------------------
2x = 4
x = 2
x + y = 7
2 + y = 7
y = 7 -2
y = 5
--------------------------------------------------
10x + y ---> 10(2) + 5 = 25

The no: is 25

Answer 2

Answer:

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)

--------------------------------------------------

Adding (1) and (2) ,

x + y = 7

x - y = -3

--------------------

2x = 4

x = 2

x + y = 7

2 + y = 7

y = 7 -2

y = 5

--------------------------------------------------

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