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.