Effect on profit or loss percentage Z when both CP (C) and SP (S) are increased by the same absolute amount: determine whether Z increases, decreases, or remains constant.

Introduction:
Profit or loss percentage depends on the ratio between profit (or loss) and cost price. When both the cost price (CP) and selling price (SP) increase by the same absolute amount, the numerator (SP - CP) does not change, but the denominator used for the percentage typically does. Understanding this sensitivity clarifies the direction of change in percentage Z.

Given Data / Assumptions:

• Original CP = C, SP = S, percentage Z is based on CP unless otherwise specified.
• Both CP and SP are increased by the same amount k.
• We consider the usual definition: profit% = (S - C)/C * 100, loss% similar.

Concept / Approach:
After adding k to both, profit in absolute terms remains (S - C). However, the new CP becomes (C + k), which increases the denominator used to compute percentage Z. A larger denominator with the same numerator yields a smaller percentage magnitude.

Step-by-Step Solution:
Original percentage: Z = (S - C)/C * 100New percentage: Z_new = (S + k - (C + k)) / (C + k) * 100Note that S + k - (C + k) = S - C (unchanged)Therefore Z_new = (S - C)/(C + k) * 100Since C + k > C for k > 0, Z_new < Z

Verification / Alternative check:
Take C = 100, S = 120 (20% profit). Add k = 10: new CP = 110, new SP = 130, profit is still 20. New profit% = 20/110 * 100 = 18.18%, which is smaller than 20%.

Why Other Options Are Wrong:

• Z increases: false because denominator increases while numerator remains the same.
• Remains constant: would require the denominator to remain unchanged, which it does not.
• None of these: incorrect because Z decreases is correct.

Common Pitfalls:

• Confusing absolute profit (unchanged) with percentage profit (changes due to the base CP).
• Using selling price as the base for the percentage instead of cost price.

Final Answer:
Z decreases