1.

the number between 10 and 100 is five times the sum of its digits. if 9 be added to it the digits are reversed find the number.

Answer»

Step-by-step explanation:

Let the number be 10 x + y

sum of its numbers =  x+ y

according to the sum

10 x + y = 5(x + y)

10 x + y = 5 x + 5 y

10 x - 5 x = 5 y - y

5 x - 4 y = 0

if 9 is added the digits are reversed

⇒ 10 x + y + 9 = 10 y + x

     10 x - x + 9 = 10 y - y

9 x - 9 y = - 9

x - y =  - 1

simultaneous equation 5 x - 4 y = 0

                                        x - y = -1

1(5 x - 4 y = 0)

5(x - y = -1)

5 x - 4 y = 0 →a

5 x - 5 y = -5→b

On subtracting b from a

5 x - 4 y = 0

- 5 x + 5 y = 5

y = 5

 

On substituting y = 5 in x - y = - 1 

we get x = 4

The number is 10 x + y = 10(4) + 5 = 45


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