7.1 Business, Financial & Consumer Mathematics

Business, Financial & Consumer Mathematics

The official NTS curriculum lists the Arithmetic block of Quantitative Reasoning as "Business Mathematics, Financial Mathematics, Consumer Mathematics, Percentage Ratio and Proportion, Zakat, Ushar and Inheritance" at 33% of the quantitative segment — 12 questions on GAT-A and GAT-C, 10 on GAT-B and GAT-D. Three of those five named items are the commercial arithmetic covered here.

Every one of these topics is a percentage in disguise. What makes them fail on the exam is not the arithmetic but the base: candidates take a percentage of the wrong number. Fix the base and the topic collapses into one skill.

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The Base Rule

If a question mixes markup and discount, the sequence is always CP → MP → SP: mark up from cost, then discount down from the marked price.

Worked Example — Markup Then Discount

A shopkeeper in Rawalpindi buys a calculator for Rs. 4,000, marks it up 25%, then advertises a 10% seasonal discount. What is the profit percentage?

$MP = 4000 \times 1.25 = 5000$ $SP = 5000 \times 0.90 = 4500$ $\text{Profit} = 4500 - 4000 = 500 \quad\Rightarrow\quad \text{Profit }\% = \frac{500}{4000}\times 100 = 12.5\%$

The planted trap is $25% - 10% = 15%$. It is wrong because the 25% is taken on 4,000 while the 10% is taken on 5,000. Different bases never subtract.

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Successive Discounts and the Multiplier Method

Convert every percentage change into a multiplier and multiply them:

Two successive discounts of 20% and 10% give $0.80 \times 0.90 = 0.72$, so the customer pays 72% and the single equivalent discount is 28%, not 30%.

The general single-equivalent formula for two discounts $a%$ and $b%$ is:

$\text{Equivalent discount} = a + b - \frac{ab}{100}$

Check: $20 + 10 - \frac{200}{100} = 28%$. ✓

The same multiplier logic answers the classic trap: a price rises 20% and then falls 20%. The result is $1.20 \times 0.80 = 0.96$, a net 4% loss, not a return to the original.

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Simple and Compound Interest

$\text{Simple Interest} = \frac{P \times R \times T}{100} \qquad\qquad \text{Compound Amount} = P\left(1 + \frac{R}{100}\right)^{n}$

Worked Comparison

Principal Rs. 50,000 at 8% per annum for 2 years.

• Simple interest: $\dfrac{50000 \times 8 \times 2}{100} = 8{,}000$
• Compound amount: $50000 \times (1.08)^2 = 50000 \times 1.1664 = 58{,}320$, so compound interest $= 8{,}320$
• Difference: Rs. 320

That difference is not a coincidence. For exactly two years:

$CI - SI = P\left(\frac{R}{100}\right)^{2}$

Check: $50000 \times (0.08)^2 = 50000 \times 0.0064 = 320$. ✓ This one-line shortcut answers a recurring NTS item type that asks for the difference without asking for either interest figure.

Compounding More Than Once a Year

When interest compounds $k$ times per year, divide the rate and multiply the periods:

$A = P\left(1 + \frac{R}{100k}\right)^{kt}$

Half-yearly compounding at 10% for one year gives $P(1.05)^2 = 1.1025P$ — an effective 10.25%, not 10%.

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Consumer Mathematics

Sales Tax

General Sales Tax is added on top of the listed price, so a tax-inclusive figure is recovered by dividing, not by subtracting. At the standard 18% rate:

• Price before tax Rs. 12,000 → payable $12000 \times 1.18 = \text{Rs. }14{,}160$
• Tax-inclusive bill Rs. 14,160 → price before tax $= \dfrac{14160}{1.18} = \text{Rs. }12{,}000$

Subtracting 18% from Rs. 14,160 gives Rs. 11,611 — the wrong answer, and a standard distractor.

Slab-Based Utility Bills

Electricity tariffs in Pakistan are charged in slabs, and only the units inside each slab pay that slab's rate. For a schedule of Rs. 10 per unit for the first 100 units, Rs. 20 for the next 100, and Rs. 30 beyond that, a household using 250 units pays:

$(100 \times 10) + (100 \times 20) + (50 \times 30) = 1000 + 2000 + 1500 = \text{Rs. }4{,}500$

Charging all 250 units at Rs. 30 gives Rs. 7,500 — the trap answer for anyone who reads only the top slab.

Instalments and Hire Purchase

Total instalment cost minus cash price is the extra charge, and it is expressed as a percentage of the amount actually financed:

A motorcycle costs Rs. 120,000 cash, or Rs. 30,000 down plus 12 monthly instalments of Rs. 8,500.

$\text{Total paid} = 30000 + (12 \times 8500) = 30000 + 102000 = 132{,}000$ $\text{Extra charge} = 132000 - 120000 = 12{,}000 \quad\text{on financed amount } 120000 - 30000 = 90{,}000$ $\text{Charge rate} = \frac{12000}{90000}\times 100 = 13.\overline{3}\%$

Habit that prevents most errors: before computing anything, write down which number is the base. Profit on cost, discount on marked price, extra charge on the amount financed, slab rate on the units inside that slab only.