The sum of two numbers is 650. If the bigger number is decreased by 4% and the smaller number is increased by 12%, then the numbers obtained are equal. The smaller number is?Options300210350240

Let's denote the smaller number as x and the larger number as y.

From the problem, we know that:

1. x + y = 650 (since the sum of the two numbers is 650)

2. y - 0.04y = x + 0.12x (since decreasing the larger number by 4% and increasing the smaller number by 12% makes them equal)

We can simplify the second equation to:

0.96y = 1.12x

Now we have a system of two equations, and we can solve it step by step.

First, let's express y from the first equation:

y = 650 - x

Now we can substitute y in the second equation:

0.96 * (650 - x) = 1.12x

This simplifies to:

624 - 0.96x = 1.12x

Adding 0.96x to both sides gives:

624 = 2.08x

Finally, dividing both sides by 2.08 gives:

x = 624 / 2.08 = 300

So, the smaller number is 300.