Question

8. A two-digit number is 4 times the sum of its digits. If 18 is added to the number, the digits
are reversed. Find the number​

Answer 1

Step-by-step explanation:

let the 2 digited number be 10x+y

Digits are x and y

sum of the digits is 4 times the number

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

4x+4y = 10x+y

4x -10x=y-4y

-6x = -3y

2x = y ------------(1)

If 18 is added to the number the digits are reversed

10x+y+18 = 10y + x

10x-x+18=10y-y

9x + 18 = 9y

x + 2 = y ----------(2)

From 1 and 2

2x = x + 2

2x-x = 2

x = 2

substitute x value in 1 or 2

2x = y

2(2) = y

y = 4

therefore required number is 10x+y

10*2 + 4 = 20 + 4 = 24

Required number is 24

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