Introduction
Profit-Loss-Discount Data Sufficiency problems ask whether the given statements provide enough information to determine values like cost price (CP), selling price (SP), marked price (MP), profit%, or discount%.
These questions focus on sufficiency of information, not on doing lengthy calculations - you must decide if a unique numerical answer can be obtained from each statement alone or only by combining them.
Pattern: Profit–Loss–Discount Based Data Sufficiency
Pattern
The key idea is to map statements into the core relations:
SP = CP × (1 + profit%),
SP = MP × (1 - discount%),
Profit% = (SP - CP) ÷ CP × 100.
Test each statement for whether it supplies all variables needed to compute the target (for example, to get CP you need SP and profit% or MP and discount% that determine SP).
Step-by-Step Example
Question
What is the cost price (CP) of an article?
(I) Selling price (SP) = ₹1,200 and profit = 20%.
(II) Marked price (MP) = ₹1,500 and discount = 20%.
Choose the correct option:
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Each statement alone is sufficient
D. Both statements together are necessary
Solution
-
Step 1: Analyze Statement (I)
SP = ₹1,200 and profit = 20% ⇒ SP = CP × (1 + 20%) = CP × 1.20.
So CP = SP ÷ 1.20 = ₹1,200 ÷ 1.20 = ₹1,000 → (I) alone is sufficient. -
Step 2: Analyze Statement (II)
MP = ₹1,500 and discount = 20% ⇒ SP = MP × (1 - 20%) = 1,500 × 0.80 = ₹1,200.
Now SP is known, and CP can be found as in (I): CP = ₹1,200 ÷ 1.20 = ₹1,000 → (II) alone is sufficient. -
Final Answer:
Each statement alone is sufficient → Option C -
Quick Check:
Both (I) and (II) independently lead to SP = ₹1,200 and CP = ₹1,000 ✅
Quick Variations
1. Given SP and discount% - find CP using CP = SP ÷ (1 + profit%) if profit% is provided elsewhere.
2. Given MP and profit% - sometimes you must convert MP → SP using discount or vice versa.
3. Two statements giving different expressions for profit% and discount% - may require combining to isolate CP or SP.
4. Worded financial contexts: successive discounts, VAT/sales tax added after discount (treat tax like an additional multiplicative factor).
Trick to Always Use
- Step 1: Convert percents to multipliers early (e.g., +20% → ×1.20; -20% → ×0.80).
- Step 2: Write the direct formula you need (e.g., CP = SP ÷ multiplier or SP = MP × multiplier).
- Step 3: Check if a single statement gives all variables required for that formula - if yes, it’s sufficient.
- Step 4: When in doubt, compute the numeric value symbolically to see if a unique answer results.
Summary
Summary
- Convert profit/discount percentages to multiplicative factors (e.g., ×1.20, ×0.80) immediately.
- One statement suffices only if it provides all inputs for the target formula (CP, SP, MP, profit%, discount%).
- Combine statements only when one provides the relation and the other provides the missing numeric value.
- Quickly verify by computing the value symbolically or numerically to confirm uniqueness.
Example to remember:
(I) SP = ₹1,200 & profit 20% ⇒ CP = ₹1,000; (II) MP = ₹1,500 & discount 20% ⇒ SP = ₹1,200 ⇒ CP = ₹1,000.
Hint: Convert profit% to multiplier (12.5% → 1.125) then divide SP by multiplier to get CP.
Common Mistakes: Assuming MP→SP info automatically gives CP without profit% data.