Question

In a two digit number the tenths digit is three times the units digit when the number is decreased by 54 the digits are reversed find the number

Answer 1

Let the number be 10a + b
According to the question in first equaton.
a = 3b..............(1)
According to the question in second equation.
10a + b - ( 10b + a ) = 54
10a + b - 10b - a = 54
( 9a - 9b ) = 54
9 ( a - b ) = 54
a - b = 54/9
a - b = 6.....................(2)
By putting the value on second equation.
a - b = 6
3b - b = 6
2b = 6
b = 6/2
b = 3.
Now,
a - b = 6
a - 3 = 6
a = 6 + 3
a = 9.
Number = 10a + b
10 × 9 + 3
90 + 3
93. Ans

Answer 2

Let the unit digit be X
Let the tens digit be Y
where Y = 3X ..........(1)
So the number will be (10Y+X)
(10Y+X) -54 = (10X+Y)
sub 1 here
( 10x3X+X) -54= (10X+3X)
( 30X+X) - 54 = (13X )
31X-54= 13X
31X-13X= 54
X (31 -13) = 54
X 18 =54
X= 54 /18
X= 3
So the number is= (10Y+X)
= (10 x 3X+X)
= (30X+X)
= (30x3+3)
= (90 +3)
So the number is 93
When it is subtracted by 54 we get the number 39 (which is the reverse of the original number)