The sum of a two digit number and the number obtained by reversing the order of digits is 132. if 12 is added to the number ,new number becomes 5 times the sum of the digits of the original number.find the number.
Answers
Answered by
6
XY + YX = 132
10X + Y + 10Y + X = 132
X + Y = 12
XY + 12 = 5×(X+Y)
5X — 4Y = —12
5×(12—Y) — 4Y = —12
60 —9Y = —12
Y = 8
X = 4
The two digit number is 48
10X + Y + 10Y + X = 132
X + Y = 12
XY + 12 = 5×(X+Y)
5X — 4Y = —12
5×(12—Y) — 4Y = —12
60 —9Y = —12
Y = 8
X = 4
The two digit number is 48
Answered by
12
Let the unit digit =x
Let the tens digit=y
No. Obtained = 10y+x
No. Obtained by reversing the digits =10x+y
According to question,
10y+x+10x+y=132
11x+11y=132
11(x+y) =132
x+y=12___________(1)
12+10y+x=5(x+y)
4x-5y=12__________(2)
Solve the equation (1) and (2)
x=8 , y=4
No. Obtained=10y+x
= 10×4+8
= 48
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