Question

If \[ p : q = 1 : 2, \quad q : r = 4 : 3, \quad r : s = 4 : 5 \] and \( u \) is 50% more than \( s \), what is the ratio \( p : u \)?

• A. 2 : 15
• B. 16 : 15
• C. 1 : 5
• D. 16 : 45

Hint:

When solving ratio problems, express all variables in terms of one common variable to simplify the calculations.

Answer 1

The Correct Option is C

Given the ratios: \[ p : q = 1 : 2 \quad \text{(i.e., } p = \frac{q}{2} \text{)} \] \[ q : r = 4 : 3 \quad \text{(i.e., } q = \frac{4r}{3} \text{)} \] \[ r : s = 4 : 5 \quad \text{(i.e., } r = \frac{5s}{4} \text{)} \] We can write all terms in terms of \( s \). Start by expressing \( p \), \( q \), and \( r \) in terms of \( s \): \[ r = \frac{5s}{4} \] \[ q = \frac{4r}{3} = \frac{4 \times \frac{5s}{4}}{3} = \frac{5s}{3} \] \[ p = \frac{q}{2} = \frac{\frac{5s}{3}}{2} = \frac{5s}{6} \] Now, \( u \) is 50% more than \( s \), so: \[ u = 1.5s \] Thus, the ratio \( p : u \) is: \[ \frac{p}{u} = \frac{\frac{5s}{6}}{1.5s} = \frac{5}{6 \times 1.5} = \frac{5}{9} = 1 : 5 \] Step 1: Conclusion
The ratio \( p : u \) is \( 1 : 5 \), so the correct answer is (C).