There are two numbers such that the sum of twice the first number and thrice the second number is 100 and the sum of thrice the first number and twice the second number is 120. Which is the larger number?

Let us assume the first number is x and second number is y.
According to question,
sum of twice the first number and thrice the second number is 100.
2x + 3y = 100 ...................(1)
and sum of thrice the first number and twice the second number is 120.
3x + 2y = 120...................(2)
Subtract equation (1) from Equation (2) after multiply 2 with Equation (1) and 3 with Equation (2), we will get.
3(3x + 2y) - 2(2x + 3y) = 3 x 120 - 2 x 100
9x + 6y - 4x - 6y = 360 - 200
5x = 160
x = 32
put the value of x in equation (1)
2 x 32 +3y = 100
3y = 100 - 64
3y = 36
y = 12
The larger Number is 32 .