# Two numbers are in the ratio of 3: 4. If 8 be subtracted from each, then the new ratio becomes 17:24. What are the two numbers?

## Two numbers are in the ratio of 3: 4. If 8 be subtracted from each, then the new ratio becomes 17:24. What are the two numbers?

**(A) 42 and 56** (B) 30 and 40 (C) 45 and 60 (D) 60 and 80

Let the two numbers be \(3x\) and \(4x\) since they are in the ratio of 3:4 (where \(x\) is the common factor).

According to the given condition, if 8 is subtracted from each number, the new ratio becomes 17:24. So, we can set up the following equation:

\[\frac{3x – 8}{4x – 8} = \frac{17}{24}\]

Now, cross-multiply to solve for \(x\):

\[24(3x – 8) = 17(4x – 8)\]

Expand and simplify:

\[72x – 192 = 68x – 136\]

Subtract \(68x\) from both sides:

\[4x – 192 = -136\]

Add 192 to both sides:

\[4x = 56\]

Divide by 4:

\[x = 14\]

Now that we have the value of \(x\), we can find the two numbers:

The first number: \(3x = 3 \times 14 = 42\)

The second number: \(4x = 4 \times 14 = 56\)

So, the two numbers are 42 and 56.