This problem requires us to find the ratio between two quantities, A and C, based on the relationships given between A, B, and C involving percentages.

Solving for the Ratio A:C

We are given two conditions:

• A exceeds B by 50%.
• B is less than C by 25%.

Step 1: Express A in terms of B

The statement "A exceeds B by 50%" means that A is equal to B plus 50% of B.

Mathematically, this can be written as:

A = B + (50% of B)

A = B + \(0.50 \times B\)

A = B \((1 + 0.50)\)

A = \(1.50B\)

Step 2: Express B in terms of C

The statement "B is less than C by 25%" means that B is equal to C minus 25% of C.

Mathematically, this can be written as:

B = C - (25% of C)

B = C - \(0.25 \times C\)

B = C \((1 - 0.25)\)

B = \(0.75C\)

Step 3: Substitute to find A in terms of C

Now, we substitute the expression for B from Step 2 into the equation for A from Step 1:

A = \(1.50B\)

Substitute \(B = 0.75C\):

A = \(1.50 \times (0.75C)\)

A = \(1.125C\)

Step 4: Calculate the ratio A:C

To find the ratio A:C, we can express the relationship A = \(1.125C\) as a fraction A/C:

\(\frac{A}{C} = 1.125\)

To express this ratio using integers, we convert the decimal 1.125 into a fraction:

1.125 = \(\frac{1125}{1000}\)

Now, we simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 125:

\(\frac{1125 \div 125}{1000 \div 125} = \frac{9}{8}\)

Therefore, the ratio A:C is 9:8.

Final Ratio

The calculated ratio of A to C is 9:8.