This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Answer
\text{72
Step 1: Set up the given ratio and the equivalent ratio with the known number. The problem states that the number 48 is to be increased in the ratio . This means that 48 corresponds to the '2' part of the ratio, and we need to find the number corresponding to the '3' part. We can write this as:
Step 2: Find the scaling factor. To find the value of , we first determine what factor was used to change 2 into 48.
Step 3: Apply the scaling factor to find the increased number. Now, multiply the second part of the ratio (3) by the same factor to find . The increased number is 72.
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Set up the given ratio and the equivalent ratio with the known number. The problem states that the number 48 is to be increased in the ratio 2:3.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.