Answer:
2 : 3
Step-by-step explanation:
Let x represent the first number and let y represent the second number.
Therefore the initial sum of the numbers = x + y
Given that the first number is increased by 30%, it becomes = x + 30% of x = x + 0.3x = 1.3x.
Also, the second number is increased by 80%, it becomes = y + 80% of y = y + 0.8y = 1.8y.
The sum of this increased numbers is 1.6 times larger than the initial sum. That is:
1.3x + 1.8y = 1.6(x + y)
1.3x + 1.8y = 1.6x + 1.6y
1.8y - 1.6y = 1.6x - 1.3x
0.2y = 0.3x
The ratio of the first number to the second number (that is x / y) is:
0.3x = 0.2y
Divide through by 0.3y:
0.3x / 0.3y = 0.2y / 0.3y
x / y = 0.2 / 0.3
x / y = 2 / 3
x : y = 2 : 3
