Explanation
Let us solve this problem step-by-step using simple algebra.
Step 1: Set up the equations
The given ratio of the two numbers is 14:25.
Let the common multiplier for the ratio be x.
Therefore, we can represent the two numbers as:
Smaller number =14x
Larger number =25x
Step 2: Use the given difference to find x
According to the problem, the difference between the larger number and the smaller number is 264.
We can write this as an equation:
25x−14x=264
Simplify the left side of the equation:
11x=264
Now, solve for x:
x=11264
x=24
Step 3: Calculate the smaller number
Now that we have the value of x, we can easily find the smaller number:
Smaller number=14x
Smaller number=14×24
Smaller number=336
Conclusion
The value of the smaller number is 336.
Hence, the correct option is (c) 336.