Two numbers are in the ratio of 6 : 8.If 10 is subtracted from each,the new numbers are in the ratio 16 : 32.Find the smaller number.22123815

Step 1: Let's denote the two numbers as 6x and 8x, where x is a common multiplier.

Step 2: According to the problem, if 10 is subtracted from each number, the ratio becomes 16 : 32. We can write this as:

(6x - 10) / (8x - 10) = 16 / 32

Step 3: Simplify the right side of the equation:

(6x - 10) / (8x - 10) = 1 / 2

Step 4: Cross multiply to solve for x:

2 * (6x - 10) = 1 * (8x - 10)

Step 5: Simplify the equation:

12x - 20 = 8x - 10

Step 6: Rearrange the equation to solve for x:

12x - 8x = 20 + 10

Step 7: Simplify the equation:

4x = 30

Step 8: Solve for x:

x = 30 / 4

x = 7.5

Step 9: Substitute x = 7.5 back into the expression for the smaller number (6x):

6x = 6 * 7.5 = 45

So, the smaller number is 45.