Question

the sumof the ten and unit digits of a two digit number is 7 ifthe digits are reversed and new number is increased by 3 then it becomes 4 times of the orginal number find the orginal number​

Answer 1

Solution :

Let the original number be ab .

a + b = 7 . . . (1)

> 2a + 2b = 14 . . .(2)

The digits are reversed .

The number number becomes ba .

If the digits are reversed and new number is increased by 3 then it becomes 4 times of the orginal number .

Thus ;

10b + a + 3 = 4( 10a + b )

> 10b + a + 3 = 40a + 4b

> 39a - 6b = 3

> 13a - 2b = 1 . . . (3)

Adding (2) and (3)

> 15a = 15

> a = 1

> b = 6

Thus , the number becomes 16 .

This is the required answer .

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Answer 2

Answer:

Required Answer :-

Let the number be xy

x + y = 14 (EQ 1)

2x + 2y = 14 (EQ 2)

Now,

when reversed the number become yx

10y + x + 3 = 4(10x + y)

10y + x + 3 = 40x + 4y

(40x - x ) - (10y - 4y) = 3

39x - 6y = 3

13x - 2y = 1 (EQ 3)

Now,

Adding (2) and 3

(13x + 2x) (2y - 2y) = 14 + 1

15x = 15

x = 1

y = 6