Percentages

Section A · Futures First International — Market Trading Intern OA

📌 What Has Been Asked (OA & Rounds)

🧠 Core Concepts

1. Percentage ↔ Fraction Equivalents (MEMORIZE)

This is the single most important table for Futures First speed math. Convert every % to a fraction before computing.

2. Basic Percentage Formulas

3. Successive Percentage Change

If value changes by a% then b%:

Examples:

• +20% then −10%: Net = 20 − 10 + (20×(−10))/100 = 10 − 2 = +8%
• +10% then +10%: Net = 10 + 10 + 100/100 = +21%
• −20% then −20%: Net = −20 − 20 + 400/100 = −36%

4. Percentage → Multiplier (Fastest Approach)

5. Reverse Percentage

"After a 20% increase, value is 600. What was the original?"

Trap: Students often do 600 − 20% of 600 = 480. WRONG. The 20% is of the original, not the final.

⚡ Speed Tricks for Futures First

Trick 1: "X% of Y = Y% of X"

• 37% of 200 = 200% of 37 = 74 ← pick whichever is easier

Trick 2: Break into easy parts

• 17.5% of 400 = 10% + 5% + 2.5% = 40 + 20 + 10 = 70
• 65% of 840 = 50% + 10% + 5% = 420 + 84 + 42 = 546

Trick 3: Use fractions for speed

• 12.5% of 960 = 1/8 × 960 = 120
• 33.33% of 729 = 1/3 × 729 = 243
• 37.5% of 480 = 3/8 × 480 = 180

Trick 4: Successive % on 100

Always think of starting with 100:

• "Price rises 20%, then falls 15%"
• 100 → 120 → 120 × 0.85 = 102 → Net = +2%

Trick 5: "Stock goes up X%, how much must it fall to return?"

• Up 25% (×5/4): must fall by 1/5 = 20% to return
• Up 50% (×3/2): must fall by 1/3 = 33.33% to return
• Up 100% (×2): must fall by 1/2 = 50% to return

Pattern: If up by x%, must fall by x/(100+x) × 100 to return.

🎯 What Can Be Asked (Variations)

1. "If A's salary is 20% more than B's, by what % is B's salary less than A's?" → B is less by 20/120 × 100 = 16.67% (= 1/6)

2. "In an election, candidate A gets 60% of votes. He wins by 2400 votes. Total votes?" → Difference = 20% (60% − 40%) = 2400 → Total = 2400/0.20 = 12,000

3. "Price of sugar rises by 25%. By what % should consumption be reduced to keep expenditure same?" → Reduce by 25/125 × 100 = 20%

4. "Successive discounts of 20% and 10% are equivalent to a single discount of ?" → Net = 20 + 10 − (20×10)/100 = 28%

5. Combined expression (classic FF style): "35% of 1240 + 62.5% of 320 = ?" → 7/20 × 1240 + 5/8 × 320 = 434 + 200 = 634

📝 Practice Questions (with Answers)

Q1. A stock price increases by 10% on Monday and decreases by 10% on Tuesday. What is the net change?

A: 10 − 10 + (10×(−10))/100 = −1. Net = −1% (you're down, not even!)

Q2. What is 87.5% of 640?

A: 7/8 × 640 = 560

Q3. A's salary is 25% less than B's. By what % is B's salary more than A's?

A: If B = 100, A = 75. B is more by 25/75 × 100 = 33.33%

Q4. After successive increases of 20% and 25%, a number becomes 900. Find the original.

A: Original × 1.2 × 1.25 = 900 → Original × 1.5 = 900 → Original = 600

Q5. 45% of ? = 270

A: ? = 270 / 0.45 = 270 × 100/45 = 270 × 20/9 = 600

Q6. If 40% of a number is 80 more than 25% of the same number, find the number.

A: 0.40N − 0.25N = 80 → 0.15N = 80 → N = 80/0.15 = 533.33

🔑 Exam Strategy

• Never do decimal multiplication — convert to fractions first
• The fraction-percentage table above is your biggest edge — other candidates waste 30+ seconds on what you can do in 5
• For "successive change" questions, use the formula a + b + ab/100 — instant answer
• For combined expressions ("35% of 1240 + ..."), the answers are MCQ — estimate first, verify only if two options are close
• In the interview/buzzer round, say the fraction conversion aloud: "37.5% is 3/8, so 3/8 of 480 is 180" — shows confidence