Correct Answer:
Option D —
ab + bc + ac
Here is the step-by-step breakdown without using math symbols:
1. Express x, y, and z in Terms of k
From the given equal ratios, x over a equals k, which means x equals a times k.
Similarly, y over b equals k, which means y equals b times k.
Likewise, z over c equals k, which means z equals c times k.
2. Substitute the Values into the Expression
The term b times x becomes b times a times k, or a times b times k.
The term c times y becomes c times b times k, or b times c times k.
The term a times z becomes a times c times k, or a times c times k.
Adding these three terms together gives k times the quantity a times b plus b times c plus a times c.
3. Divide by k
Dividing the combined total by k cancels out k.
This leaves a times b plus b times c plus a times c.
Conclusion
Correct Answer: D) ab + bc + ac
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
