Question 146474: A two digit no is obtained by either subtracting 12 from 4 times the sum of its digits or by adding 6 to twicethe difference of its digits. Find the no.
(1)16 (2)28 (3)39 (4)can't be determined.....
Answer by aswathytony(47)   (Show Source):
You can put this solution on YOUR website! let the digit in tens place be x and that in ones place is y.so the two digit no is 10x +y. (ex: 56 = 5*10 +6)
given 12 is subtracted from four times sum of digits gives the number:
i.e 4 ( x+y) -12 = 10x + y (digits are x & y , so sum =x+y)
also, adding 6 to twice the difference gives the number
i.e. 2 ( y - x) + 6 = 10x + y .( consider that tens place digit is less than ones place digit, if u put x - y , you will end up in negative answers, so take y-x)
i.e , 4 (x + y ) -12 = 2(y-x) +6 (since RHS are equal, LHS are also equal)
4x + 4y -12 = 2y -2x +6
4x+2x +4y -2y -12-6 =0
6x + 2y -18 = 0
divide by 2 ; 3x + y - 9 =0
y = 9 - 3x
substitute y = 9-3x in eq: 4 ( x+y) - 12 = 10x +y
4 ( x + 9 - 3x ) -12 = 10x + 9-3x
4x + 36 -12x -12 = 7x +9
-8x + 24 = 7x + 9
24-9 = 7x +8x
15 = 15x
x = 15 / 15 = 1
put x=1 in y =9-3x and find y
y= 9-3*1= 9-3 =6
so the number is 10x + y = 10*1 + 6 = 10+6 =16.
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