20% then 10% is not 30% off — the second cut is smaller than it looks.
The problem
A shirt priced at ₱500 is discounted by 20%. The sale price is then discounted by a further 10%. What is the final price?
Take them in order: 500 × 0.8 = 400, then 400 × 0.9 = ₱360. B adds the discounts into 30%, but the second cut lands on the reduced ₱400, not the original ₱500. Successive percentages multiply; they never add.
Paying is easier to track than saving.
keep 0.80
keep 0.90
100% − 20% = 80%
Subtracting works too, but it takes two steps each time. Multiplying by what you keep does it in one.
0.20 · 500 = 100
the saving
500 − 100 = 400
what you actually pay
or in one move
0.80 · 500 = 400
this is the SALE price, not the final one
10% of 400 = 40
10% of 500 = 50
that price is gone
Each discount acts on whatever the price is at that moment. Discounts never stack onto the original.
0.10 · 400 = 40
the second saving
400 − 40 = 360
the final price
or in one move
0.90 · 400 = 360
Skip the middle price entirely.
500 · 0.80 · 0.90 = 360
original · keep 80% · keep 90%
0.80 · 0.90 = 0.72
you pay 72%, so the real saving is 28%
30% off » ₱350
28% off » ₱360
The missing 2% is the 10% that was never charged on the ₱100 you already saved.
After successive discounts of 25% and 10%, a jacket sells for ₱2,025. What was the original price?
0.75 × 0.90 = 0.675
the buyer pays 67.5% of the original
0.675 × P = 2,025
the final price is a part of P
P = 2,025 ÷ 0.675 = ₱3,000
divide, never add percents back
2,025 × 1.35 ≈ ₱2,734 — the discounts were taken from the original, so putting them back on the smaller final price undershoots. Check forwards instead: 3,000 × 0.75 = 2,250, then 2,250 × 0.90 = 2,025 ✓.
Three discounts, one of them 12.5%. A ₱4,800 tablet gets successive discounts of 20%, 12.5% and 5%. Find the final price and the single equivalent discount.
keep: 0.80 × 0.875 × 0.95
12.5% off keeps 87.5%
0.80 × 0.875 = 0.70; 0.70 × 0.95 = 0.665
pair the easy ones first
4,800 × 0.665 = ₱3,192
the final price
1 − 0.665 = 33.5% off
not 20 + 12.5 + 5 = 37.5%
What is different: three factors and a decimal percent. The chain just gets one link longer.
Up first, then down by the same percent. A price is raised 25%, then the new price is cut 25%. What is the net change?
1.25 × 0.75 = 0.9375
a rise keeps 125%
1 − 0.9375 = 0.0625
below where it started
a 6.25% decrease
on ₱800: 1,000, then 750
What is different: one multiplier is above 1. The cut is taken from the bigger, raised price, so the two changes do not cancel.
+25% and −25% look like they cancel, but 25% of ₱1,000 is more than 25% of ₱800. Doing the cut first and the rise second gives the same 0.9375 — order never matters, only the multipliers.
Successive discounts of 25% and x% equal a single discount of 40%. Find x.
0.75 × (keep) = 0.60
a 40% discount keeps 60%
keep = 0.60 ÷ 0.75 = 0.80
the second multiplier
x = 20
keeping 80% is 20% off
40 − 25 = 15 is the trap answer. The same multipliers handle a markup first: marked 25% above cost, then 10% and 10% off, sells at 1.25 × 0.9 × 0.9 = 1.0125 of cost — a profit of just 1.25%.
Every successive-discount item is one product of multipliers: final = original × keep₁ × keep₂. Forward questions multiply; “original price” questions divide; an unknown discount is the missing factor. The 10-second check: your answer's single equivalent discount must be a little less than the two percents added.
140 ÷ 500 = 0.28 » 28% off
and 500 − 140 = 360
Practice problem
A jacket priced at ₱800 is discounted by 25%. The sale price is then increased by 10% for tax. What is the final price?
800 × 0.75 = 600, then 600 × 1.1 = ₱660. C treats it as a net −15% of 800. The tax is charged on the discounted ₱600, so it adds only ₱60 — the two percentages sit on different bases.
Hint: one goes down and one goes up. An increase means you keep more than 100%, so its multiplier is bigger than 1.
