Sub-duplicate Ratio: Find 𝑥² When 𝑝 : 𝑞 Is the Sub-duplicate Ratio of (𝑝 − 𝑥²) : (𝑞 − 𝑥²)

In this post, we explore how to solve for 𝑥² using the sub-duplicate ratio concept. This type of problem commonly appears in aptitude-based exams and helps test your grasp on ratio transformations and algebraic manipulation.

📌 Given: 

𝑝 : 𝑞 is the sub-duplicate ratio of (𝑝 − 𝑥²) : (𝑞 − 𝑥²)

📖 By definition,  

If 𝑎 : 𝑏 is the sub-duplicate ratio of 𝐴 : 𝐵, then:

𝑎 : 𝑏 = √𝐴 : √𝐵  

⇒ 𝑎² : 𝑏² = 𝐴 : 𝐵

Apply this to the given: 

𝑝 : 𝑞 = √(𝑝 − 𝑥²) : √(𝑞 − 𝑥²)

Now squaring both sides: 

𝑝² : 𝑞² = (𝑝 − 𝑥²) : (𝑞 − 𝑥²)

From here, cross-multiply and simplify to find the value of 𝑥².

📹 Watch full explanation in the video below:🎥

If p : q is the sub-duplicate ratio of p–x^2 : q–x^2 then x^2 is ?

🎯 Useful For These Exams

✅ Indian Exams:

• CA Foundation

• CUET (Quantitative Aptitude)

• CSEET

• CMA Foundation

• SSC CGL, CHSL

• RRB NTPC

• Banking (IBPS, SBI PO/Clerk, RBI Assistant)

• State PSC aptitude papers

🌍 International Exams:

• SAT Math

• ACT Math

• GRE Quant

• GMAT Quant

• IGCSE / GCSE Math

• Foundation-level Math Olympiads

  
  

💡 Quick Tip:

Always remember:If 𝑎 : 𝑏 is the sub-duplicate ratio of 𝐴 : 𝐵, then 𝑎² : 𝑏² = 𝐴 : 𝐵.Use this identity to reverse engineer any sub-duplicate relationship.

🧪 Try Yourself:

If 𝑝 : 𝑞 is the sub-duplicate ratio of (𝑝 − 𝑥²) : (𝑞 − 𝑥²), what is the value of 𝑥²?

Comment your answer below!