SATHEE: Percentages Master

Percentages Master - Quick Revision

1 % = 1⁄100; shift decimal two places left to convert % → decimal.
x % of y = x × y ÷ 100 (always divide last).
“What % is A of B?” → (A ÷ B) × 100.
Percentage increase = (change ÷ original) × 100.
Percentage decrease = (change ÷ original) × 100.
New after p % increase = original × (1 + p⁄100).
New after p % decrease = original × (1 – p⁄100).
Successive changes a % then b %: net = a + b + ab⁄100.
If price ↑ p %, consumption ↓ by (100p⁄100+p)% to keep budget same.
CP → MP → Discount → SP chain: always apply % on immediate previous value.
Profit % = (profit ÷ CP) × 100.
Loss % = (loss ÷ CP) × 100.
Population after n years at r % p.a. = P(1 + r⁄100)ⁿ.
Compound half-yearly: rate → r⁄2, time → 2n.
Equivalent single discount of d₁% & d₂% = d₁ + d₂ – d₁d₂⁄100.
Article sold at x% profit & y% loss finally breaks even ⇒ CP ratio = y : x.
Percentage point ≠ percent; 20 % → 25 % is +5 percentage points, +25 % in value.
To find original before x % increase: divide by (1 + x⁄100).
100 % of a number = the number itself; 50 % = half; 25 % = quarter.
In exams, 90 % questions come from variants of above 19 rules—master them!

Formula	Use
p % of A = A × p ÷ 100	Quick value extraction
(New – Old) ⁄ Old × 100	% change (increase/decrease)
Old = New × 100 ⁄ (100 ± p)	Reverse % calculation
Net % change = x + y + xy⁄100	Successive changes
Single equivalent discount = d₁ + d₂ – d₁d₂⁄100	Two successive discounts
Consumption reduction % = (100 × p) ⁄ (100 + p)	Price rise offset
Population/Amount A = P(1 ± r⁄100)ⁿ	Compound growth/decay
CI – SI ≈ P(r⁄100)² for 1 yr	Quick diff CI-SI
If a % profit & b % loss give 0 net, CP₁ : CP₂ = b : a	Equal money balance
MP = CP × (100 + p) ⁄ (100 – d)	Link CP, profit%, discount%

“Dr. PP” – Decimal → Percent: Push point 2 places Right; Percent → Decimal: Pull 2 places Left.
“IS-LD” – Increase: Add (1 + p⁄100); Decrease: Less (1 – p⁄100).
“SAAD” – Successive changes Add, then Add Product (x+y+xy⁄100).
“50-25-12.5” – Halve each time for quick mental fractions.
“CIPD” – CI ≈ SI + (SI×rate)⁄200 for 2 yrs (ballpark).

Error	Correct
Taking % of wrong base (new instead of original)	Always divide change by original value
Adding discounts directly (30%+20%=50%)	Use d₁+d₂–d₁d₂⁄100 → 44 %
Confusing percentage point with percent	10 % → 15 % is +5 points but 50 % increase
Applying increase formula for decrease	Use minus sign: (1 – p⁄100)
Forgetting to convert % to decimal in CI formula	Write 8 % as 0.08, not 8

Question 1

A shirt priced ₹800 is marked up 25 % then discounted 20 %. What is final price? A) 760 B) 800 C) 840 D) 720 **Answer: B) 800**

Question 2

If 30 % of x = 45, then x is: A) 120 B) 135 C) 150 D) 180 **Answer: C) 150**

Question 3

Population increases 10 % yearly. After 2 years it is 12100. Initial population was: A) 10000 B) 10500 C) 11000 D) 11500 **Answer: A) 10000**

Question 4

Successive discounts of 20 % and 10 % equal a single discount of: A) 30 % B) 28 % C) 25 % D) 24 % **Answer: B) 28 %**

Question 5

A man loses 10 % on selling price. His loss % on cost price is approximately: A) 9 % B) 10 % C) 11.11 % D) 12.5 % **Answer: C) 11.11 %**