The arithmetic is easy. Knowing which number to divide by is the whole subject.
Find the true cost
A phone costs ₱12,000 cash. On terms it is ₱2,000 down and ₱950 a month for 12 months. How much extra does buying on terms cost?
The instalments come to 12 × 950 = ₱11,400, and adding the deposit gives a total of ₱13,400. Against the cash price of ₱12,000 that is ₱1,400 extra. D forgets the deposit is part of what you pay. C mistakes the deposit for the extra cost — the deposit is money off the price, not a charge.
1
What you earn, and what you actually take home.
Term
Means
Example
Wage
paid per hour or per day
₱75/hour × 8 hours = ₱600
Salary
a fixed amount per month
₱18,000 a month
Commission
a percent of what you sell
4% of ₱50,000 = ₱2,000
Overtime
a higher rate past normal hours
₱75 × 1.25 = ₱93.75/hour
Gross pay
before deductions
₱18,000
Net pay
after SSS, PhilHealth, Pag-IBIG, tax
what reaches the bank
Gross and net are the pair people confuse in real life. A job advertised at ₱18,000 does not put ₱18,000 in your hands.
2
Profit and loss are measured against the cost.
percent profit = profit ÷ cost price × 100
buy at ₱250, sell at ₱325
a sari-sari store item
profit = ₱75
325 − 250
75 ÷ 250 = 0.30
divide by what it cost you
= 30% profit
the mark-up
Cost price, not selling price
Dividing ₱75 by ₱325 gives about 23%, which is the margin — a different
and smaller number that answers a different question. At this level, percent
profit always means profit over cost.
3
Best buys: reduce everything to one unit.
Price per gram, per litre, per piece — whatever they share.
Pack
Price
Per 100 g
250 g
₱48.00
₱19.20
400 g
₱72.00
₱18.00
1 kg
₱195.00
₱19.50
The 400 g pack wins at ₱18.00 per 100 g. Note what the table kills: the biggest
pack is not the cheapest here, which is exactly why the calculation is worth
doing.
Either divide price by quantity, or quantity by price. Just be consistent — with price ÷ quantity, smaller is better.
4
Buying on terms: add up everything you hand over.
total paid = deposit + (instalment × number of instalments)
extra = 13,400 − 12,000 = ₱1,400
the cost of paying later
1,400 ÷ 12,000 = 0.1167
as a fraction of the cash price
≈ 11.7%
the interest rate
Terms are not automatically a bad deal — sometimes ₱950 a month is simply possible
when ₱12,000 at once is not. But the extra should be a decision, not a surprise.
5
Which number goes on the bottom.
Almost every mistake in this topic is a wrong denominator.
Percent profitprofit ÷ cost pricewhat you put in
Percent discountdiscount ÷ original pricebefore the cut
Interest rate on termsextra ÷ cash pricewhat it would have cost
Commission ratecommission ÷ salesthe amount sold
Remember the flow
Find the change · Decide what it is a change from · Divide by that · × 100
The denominator is always the starting figure, never the one you ended with.
6
Discounts on discounts, and simple interest.
A second discount comes off the already-reduced price.
A ₱1,500 bag is marked 20% off, then a further 15% off at the counter. What is the final price?
1,500 × 0.80 = ₱1,200
20% off leaves 80%
1,200 × 0.85 = ₱1,020
15% off the NEW price
20% + 15% is not 35% off
Adding the percents gives 1,500 × 0.65 = ₱975, ₱45 too little. The 15% is taken from ₱1,200, not from ₱1,500, so the two discounts together come to 32%, not 35%.
How much is owed on an ₱8,000 loan at 5% simple interest for 4 years?
I = P × r × t
principal × rate × time in years
= 8,000 × 0.05 × 4 = ₱1,600
the interest
total = 8,000 + 1,600 = ₱9,600
principal plus interest
Simple interest is the same amount every year — here ₱400 a year — because it is always worked out on the original ₱8,000.
7
Working backwards: find the cost from the selling price.
Selling price = cost × (1 + profit rate), or cost × (1 − loss rate). Divide to go back.
An item sells for ₱690 at a 15% profit. What did it cost?
690 = 1.15 × cost
selling price is 115% of cost
cost = 690 ÷ 1.15 = ₱600
divide by the multiplier
Check forward: 600 × 1.15 = 690 ✓.
Taking the percent of the selling price
15% of ₱690 is ₱103.50, and 690 − 103.50 = ₱586.50. Check forward: 586.50 × 1.15 = 674.48, not 690. The 15% was a percent of the cost, which is the number we do not know yet — so divide, do not subtract.
An item sells for ₱340 at a 15% loss. What did it cost?
340 = 0.85 × cost
a 15% loss leaves 85%
cost = 340 ÷ 0.85 = ₱400
check: 400 × 0.85 = 340 ✓
8
Variations: salary plus commission, unlike units, breaking even.
The same few formulas, in three everyday settings.
A salesperson earns ₱12,000 a month plus 3% commission. This month she sold ₱85,000. What is her gross pay?
0.03 × 85,000 = ₱2,550
commission
12,000 + 2,550 = ₱14,550
salary plus commission
The 3% applies to the sales only, never to the salary.
Which is the better buy: 1.5 L of juice for ₱78, or 500 mL for ₱27?
78 ÷ 1.5 = ₱52 per litre
the big bottle
500 mL = 0.5 L, 27 ÷ 0.5 = ₱54 per litre
convert first
The 1.5 L bottle is cheaper per litre. Change both to the same unit before dividing.
A vendor buys 40 pieces of turon for ₱480 in all. Five are spoiled. What is the least whole-peso price per piece that avoids a loss?
pieces left to sell = 35
40 − 5
480 ÷ 35 = 13.71…
price to break even exactly
least whole peso: ₱14
round up
At ₱13 she takes 35 × 13 = ₱455, a loss; at ₱14 she takes ₱490 ✓. Breaking even means selling price total = cost total.
On the exam
Business maths items are short word problems: percent profit or loss, a discounted or marked-up price, a best buy, total pay with overtime or commission, simple interest, or the true cost of buying on terms. The fastest route is to decide which figure is the starting one and divide by it; for a backwards problem, divide by the multiplier (1.15, 0.85). For a 10-second check, run your answer forward — cost × 1.15 must give back the selling price.
Now you try
Practice problem
Find the percent loss
A vendor buys mangoes for ₱1,800 and, because some spoil, sells the lot for ₱1,530. What is the percent loss?
The loss is 1,800 − 1,530 = ₱270, and percent loss divides by the cost price: 270 ÷ 1,800 = 0.15, so 15%. B divides by the selling price instead. D is the fraction of the cost that was recovered, not the loss. C mistakes the peso loss for a percent.
Hint: a loss is still measured against what the goods cost you.
Sanity-check it — losing about a seventh of ₱1,800 should be a smallish percent.
