a number consist of 2 digits the digit in the unit place is thrice that inthe ten's place and if 1 is added to sum of the digits the addition is equal to onethird of the number.find the number
1/3(10t + u ) = t + u + 1
3t = u
1/3 (10t + 3t) =t + 3t +1
1/3 13t = 4t + 1
13t = 12t + 3
t = 3
u = 9
check: 1/3(39) = 3 + 9 + 1
yes 13 = 13
To find the number, let's start by assigning variables to the digits in the number.
Let's call the digit in the unit place "x" and the digit in the tens place "3x" since the digit in the unit place is thrice that of the tens place.
So, the number can be expressed as 3x + x = 10(3x) + x.
The problem also states that if 1 is added to the sum of the digits, then the sum is equal to one-third of the number. Mathematically, this can be written as: 1 + (3x + x) = (1/3) * (10(3x) + x).
Simplifying the equation, we have: 4x + 1 = (1/3) * (30x + x).
Multiplying through by 3 to eliminate the fraction, we get: 12x + 3 = 31x.
Moving the 12x to the right side, we have: 3 = 31x - 12x.
Simplifying, we have: 3 = 19x.
Dividing both sides by 19, we find: x = 3/19.
Since x represents a digit, it should be a whole number. However, 3/19 is not a whole number. This means that there is no solution for this problem.