Profit & Loss, Discount, Interest & Partnership

You already know percentages from Chapter 1. This chapter simply takes that one idea to the marketplace — a shop, a bank, a business. Profit and loss is a percentage on the cost price. Discount is a percentage on the marked price. Interest is a percentage on the principal. Partnership is a ratio of capital × time. Four bases, four formula families, and almost every question in the paper. Everything below is worked out with the arithmetic shown, so read with a pen — do not just read the answer, watch the numbers move.

Cost Price, Selling Price & the One Golden Rule

Cost price (CP) is what the seller paid. Selling price (SP) is what the buyer paid. If SP > CP there is profit = SP − CP; if SP < CP there is loss = CP − SP. The golden rule that decides half the marks in this chapter: profit% and loss% are always calculated on the CP, never on the SP.

Worked example. A cycle is bought for ₹800 and sold for ₹920. Profit = 920 − 800 = ₹120. Profit% = (120 ÷ 800) × 100 = 0.15 × 100 = 15%. Note the denominator: 800, the CP. Had we wrongly divided by 920 we would have got 13.04% — a wrong option that examiners love to print.

⚠️ The denominator is always CP
Profit% = (Profit ÷ CP) × 100 and Loss% = (Loss ÷ CP) × 100. Traders in real life often quote "margin" on the selling price, but in the exam, unless the question says "profit on selling price", the base is the cost price. One wrong denominator = one lost mark.

Going forward from CP, use SP = CP × (100 ± p)/100 — plus for profit, minus for loss. Example: CP = ₹1,250 with 16% profit → SP = 1250 × 116/100 = 145000/100 = ₹1,450. Example: CP = ₹2,400 with 15% loss → SP = 2400 × 85/100 = 204000/100 = ₹2,040.

One CP of ₹1,000, four situations — see the multiplier at work
SituationCalculationSelling price
20% profit1000 × 120/100₹1,200
8% profit1000 × 108/100₹1,080
5% loss1000 × 95/100₹950
15% loss1000 × 85/100₹850

Coming backwards from SP is the commoner exam question. Turn the formula upside down: CP = SP × 100/(100 ± p). Worked: an article sold for ₹1,449 gives a 15% profit → CP = 1449 × 100/115 = 144900/115 = ₹1,260. Check it: 1260 × 1.15 = 1449. ✓ Worked (loss): an article sold for ₹2,160 gives a 10% loss → CP = 2160 × 100/90 = 216000/90 = ₹2,400. Check: 2400 × 0.90 = 2160. ✓

⚠️ Exam trap
Never find CP by subtracting the percentage from the SP. For SP = ₹1,449 at 15% profit, the tempting move is 1449 − 15% of 1449 = 1449 − 217.35 = ₹1,231.65. Wrong. The 15% was charged on ₹1,260, not on ₹1,449. Always divide by (100 + p)/100; never subtract.

Two-step example (a favourite). A shirt sold for ₹720 causes a 10% loss. At what price should it be sold to make a 15% profit? Step 1 — find the CP: 720 × 100/90 = ₹800. Step 2 — new SP: 800 × 115/100 = ₹920. Whenever a question links two selling prices, the CP is the bridge. Find it first, always.

The Four Classic Profit-Loss Traps

Beyond the basic formula, every exam recycle the same four situations. Each one looks like common sense and each one punishes common sense. Learn them as stories, not as formulas.

Trap 1 — two articles sold at the same price. A man sells two watches, each for ₹1,200. On one he gains 20%, on the other he loses 20%. Gut feeling says "they cancel — no profit, no loss". Compute it. Watch A: CP = 1200 × 100/120 = ₹1,000. Watch B: CP = 1200 × 100/80 = ₹1,500. Total CP = 1000 + 1500 = ₹2,500; total SP = 1200 + 1200 = ₹2,400. So loss = ₹100, and loss% = (100 ÷ 2500) × 100 = 4% loss.

⚠️ It is ALWAYS a loss of (x/10)² per cent
Two articles at the same selling price, one at +x% and one at −x%, always give a net LOSS of (x/10)²% — never a profit, never a break-even. For x = 20: (20/10)² = 2² = 4% loss, exactly what we computed. For x = 10: (10/10)² = 1% loss. For x = 30: (30/10)² = 9% loss. Why a loss? Because the loss falls on the bigger cost price (₹1,500) while the gain falls on the smaller one (₹1,000).

Trap 2 — profit on cost vs profit on selling price. Take CP = ₹100 and a 25% profit on cost: SP = ₹125, profit = ₹25. Now express that same ₹25 as a fraction of the SP: 25 ÷ 125 = 1/5 = 20%. So "25% on cost" and "20% on selling price" are the same deal. The conversions: profit p% on CP = 100p/(100 + p) % on SP → 100 × 25/125 = 20%. And margin m% on SP = 100m/(100 − m) % on CP → 100 × 20/80 = 25%. ✓

Trap 3 — the dishonest shopkeeper. A grocer sells at his cost price but uses a weight of only 900 g in place of 1 kg. Where is the profit? Suppose his goods cost ₹1 per gram. A customer pays ₹1,000 for "1 kg" but receives 900 g, which cost the grocer only ₹900. Profit = ₹100 on a cost of ₹900 → (100 ÷ 900) × 100 = 11 1/9 % ≈ 11.11%. The formula: gain% = error/(true weight − error) × 100 = 100/(1000 − 100) × 100. With an 800 g weight: 200/800 × 100 = 25% gain.

Trap 4 — mark up first, then discount. A trader marks his goods 40% above cost and then allows a 25% discount. Is he losing money? Take CP = ₹1,200. Marked price = 1200 × 1.40 = ₹1,680. Selling price = 1680 × 0.75 = ₹1,260. Profit = 1260 − 1200 = ₹60 → 60/1200 = 5% profit. The 25% was taken on ₹1,680, not on ₹1,200 — that gap is his profit.

🧠 Reuse the successive-change formula
Chapter 1 gave you net = a + b + ab/100 for two successive changes. Trap 4 is exactly that with a = +40 and b = −25: net = 40 − 25 + (40 × −25)/100 = 15 − 10 = +5%. One line, no rupees needed. Markup-then-discount questions can always be finished in your head this way.

Marked Price & Discount

Marked price (MP), also called list price or printed price, is the tag on the article. Discount = MP − SP, and critically, Discount% = (Discount ÷ MP) × 100 — the base here is the MP, not the CP. So the chapter now has two different bases: profit sits on CP, discount sits on MP. Keep them separate and you will never be confused again.

💡 Think of it like this
Think of a clothes shop in Patna. The tag says ₹1,500 — that is the MP. The board says "12% off" — that is the discount, computed on the tag. You pay 1500 × 88/100 = ₹1,320 — that is the SP. What the shopkeeper originally paid the wholesaler, say ₹1,100, is the CP, and he never prints it anywhere. Three prices, three roles: MP is what he asks, SP is what he gets, CP is what he paid.

Successive discounts never add up. A saree is marked ₹2,000 and the shop gives 20% and then a further 10%. Step by step: after 20%, price = 2000 × 0.80 = ₹1,600; after a further 10% on ₹1,600, price = 1600 × 0.90 = ₹1,440. Total discount = 2000 − 1440 = ₹560, i.e. (560 ÷ 2000) × 100 = 28%, not 30%. The single equivalent discount formula: a + b − ab/100 = 20 + 10 − (20 × 10)/100 = 30 − 2 = 28%. ✓

Successive discounts and their single equivalent (verified on a marked price of ₹1,000)
Successive discountsSingle equivalentPrice paid on MP ₹1,000
10% + 10%19%₹810
20% + 10%28%₹720
30% + 10%37%₹630
20% + 20%36%₹640
25% + 20%40%₹600
25% + 25%43.75%₹562.50
10% + 10% + 10%27.1%₹729
20% + 10% + 5%31.6%₹684

For three discounts, apply the two-discount formula twice. Take 20%, 10% and 5%. First pair: 20 + 10 − 2 = 28%. Now combine 28% with 5%: 28 + 5 − (28 × 5)/100 = 33 − 1.4 = 31.6%. Verify on ₹2,000: 2000 × 0.80 × 0.90 × 0.95 = 1440 × 0.95 = ₹1,368, and (2000 − 1368)/2000 × 100 = 632/2000 × 100 = 31.6%. ✓ The order of the discounts never changes the answer, because multiplication is commutative.

The reverse question — fixing the MP to protect a target profit. A shopkeeper wants a 25% profit even after giving a 20% discount. His CP is ₹800. What should he mark? Required SP = 800 × 125/100 = ₹1,000. But SP = MP × 80/100, so MP = 1000 × 100/80 = ₹1,250. Check: 1250 × 0.80 = ₹1,000 = 800 × 1.25. ✓ The formula worth memorising: MP = CP × (100 + profit%)/(100 − discount%) = 800 × 125/80 = ₹1,250.

⚠️ A big discount is not a loss
"Flat 50% off" does not mean the shop is selling below cost. If the MP is set at three times the CP, then a 50% discount still leaves SP = 1.5 × CP, i.e. a 50% profit. Discount% and profit% are measured on different bases, so they can never be compared directly or subtracted from one another. Whenever a question mixes them, take CP = ₹100 and walk through the rupees.

Simple Interest — Growth in Equal Steps

In simple interest the interest is charged on the original principal every single year, so the same rupee amount is added each year. The formula is SI = (P × R × T)/100 and Amount A = P + SI. Worked: P = ₹12,000, R = 9% per annum, T = 4 years. SI = (12000 × 9 × 4)/100 = 432000/100 = ₹4,320. Amount = 12000 + 4320 = ₹16,320. Notice: ₹1,080 of interest in each of the four years — equal steps.

The same formula, rearranged, answers all four question types. Finding the rate: ₹7,500 earns ₹2,700 in 3 years → R = (100 × SI)/(P × T) = (100 × 2700)/(7500 × 3) = 270000/22500 = 12%. Finding the time: ₹6,400 earns ₹1,536 at 8% → T = (100 × 1536)/(6400 × 8) = 153600/51200 = 3 years. Finding the principal: SI of ₹2,100 at 7% for 5 years → P = (100 × 2100)/(7 × 5) = 210000/35 = ₹6,000.

Doubling and tripling. A sum doubles when the interest equals the principal, i.e. SI = P. Put that in the formula: P = (P × R × T)/100 → R × T = 100. Tripling means SI = 2P → R × T = 200. In general, to become n times, R × T = (n − 1) × 100. Worked: at 8% per annum, money doubles in T = 100/8 = 12.5 years and triples in 200/8 = 25 years.

Worked example (very common). A sum doubles itself in 8 years at simple interest. In how many years will it become four times? First find the rate: R × 8 = 100 → R = 12.5%. Four times means R × T = (4 − 1) × 100 = 300 → T = 300/12.5 = 24 years.

🧠 The staircase shortcut
Under simple interest each "extra principal" of growth takes the same number of years. If a sum doubles in 8 years, it has added 1P in 8 years — so it adds another 1P in the next 8. Triples in 16 years, four times in 24, five times in 32. No rate calculation needed at all. Remember the pattern: doubles in T → n times in (n − 1) × T years.
How long a sum takes to grow, at 8% simple interest
BecomesNeeds R × T =Time at 8%
2 times10012.5 years
3 times20025 years
4 times30037.5 years
5 times40050 years

Compound Interest — Interest on Interest

In compound interest, each year the interest is added to the principal and the next year's interest is charged on that bigger amount. Formula: A = P(1 + R/100)ⁿ and CI = A − P. Worked: P = ₹8,000, R = 10%, n = 2 years. Year 1: interest = ₹800 → amount ₹8,800. Year 2: interest = 10% of 8,800 = ₹880 → amount ₹9,680. By formula: 8000 × (1.1)² = 8000 × 1.21 = ₹9,680, so CI = ₹1,680. Simple interest for the same case would be (8000 × 10 × 2)/100 = ₹1,600 — CI is ₹80 more, and that ₹80 is exactly the interest on the first year's ₹800.

For 3 years at the same 10%: A = 8000 × (1.1)³ = 8000 × 1.331 = ₹10,648, so CI = ₹2,648 (against SI of ₹2,400). And the formula runs backwards too: if a sum amounts to ₹9,680 in 2 years at 10% compounded annually, then P = 9680 ÷ 1.21 = ₹8,000.

Half-yearly and quarterly compounding. The rule is simple: halve the rate and double the periods for half-yearly; quarter the rate and multiply the periods by four for quarterly. Worked (half-yearly): P = ₹8,000 at 10% per annum for 1.5 years → rate 5% per half-year, 3 periods. 8000 → 8400 → 8820 → ₹9,261, so CI = ₹1,261. Worked (quarterly): P = ₹16,000 at 20% per annum for 6 months → rate 5% per quarter, 2 periods. 16000 → 16800 → ₹17,640, so CI = ₹1,640.

⚠️ Half-yearly is not the same rate
Students halve the rate but forget to double the periods, or double the periods and forget to halve the rate — both give nonsense. Check yourself with this fact: ₹10,000 at 10% per annum for one year gives ₹1,000 as annual CI, but compounded half-yearly it gives 10000 × (1.05)² − 10000 = 11025 − 10000 = ₹1,025. So "10% compounded half-yearly" is really 10.25% a year. More frequent compounding always earns a little more.

The most asked formula in the whole chapter: the difference between CI and SI for 2 years = P(R/100)². Worked: P = ₹15,000, R = 8%, T = 2 years. Difference = 15000 × (8/100)² = 15000 × 0.0064 = ₹96. Long check: CI amount = 15000 × (1.08)² = 15000 × 1.1664 = ₹17,496 → CI = ₹2,496; SI = (15000 × 8 × 2)/100 = ₹2,400; difference = 2496 − 2400 = ₹96. ✓ Same answer in one step instead of five.

The formula works in reverse too, which is how the exam usually asks it. The difference between CI and SI on a sum for 2 years at 5% per annum is ₹25. Find the sum. → 25 = P × (5/100)² = P × 0.0025 → P = 25 ÷ 0.0025 = ₹10,000. Check: CI = 10000 × 1.1025 − 10000 = ₹1,025; SI = ₹1,000; difference ₹25. ✓ For 3 years the difference is P(R/100)² × (300 + R)/100. Worked with P = ₹8,000, R = 10%: 8000 × 0.01 × 310/100 = 80 × 3.1 = ₹248 — and indeed CI(3 yr) ₹2,648 − SI(3 yr) ₹2,400 = ₹248. ✓

Depreciation and population growth are just CI with a different name. For a value that falls year on year, use A = P(1 − R/100)ⁿ. A machine worth ₹50,000 depreciating at 10% a year is worth 50000 × (0.9)² = 50000 × 0.81 = ₹40,500 after 2 years. For a value that rises, use the plus sign: a town of 62,500 people growing at 4% a year becomes 62500 × (1.04)² = 62500 × 1.0816 = 67,600 in 2 years (step by step: 62,500 → 65,000 → 67,600). Backwards: if the population is now 67,600 after two years of 4% growth, two years ago it was 67600 ÷ 1.0816 = 62,500.

Instalments. When a debt is repaid in equal annual instalments under CI, each instalment must be discounted back to today: Debt = x/(1 + R/100) + x/(1 + R/100)² + … Worked: what equal annual instalment clears a debt of ₹10,500 in 2 years at 10% per annum CI? x/1.1 + x/1.21 = 10500. Try x = ₹6,050: 6050/1.1 = ₹5,500 and 6050/1.21 = ₹5,000, total ₹10,500. ✓ So the instalment is ₹6,050. Ledger check: 10500 × 1.1 = 11,550, pay 6,050 → ₹5,500 left; 5500 × 1.1 = 6,050, pay 6,050 → nil. ✓

Partnership — Capital × Time

When two or more people run a business together, the profit is shared in the ratio of what each one actually contributed. If everybody's money stays in for the same length of time, it is a simple partnership and the profit ratio is just the ratio of capitals. Worked: A, B and C invest ₹40,000, ₹60,000 and ₹80,000 for one year. Ratio = 40 : 60 : 80 = 2 : 3 : 4, total 9 parts. A profit of ₹36,000 → one part = 36000/9 = ₹4,000 → A ₹8,000, B ₹12,000, C ₹16,000. Check: 8000 + 12000 + 16000 = ₹36,000. ✓

If the money stays in for different lengths of time, it is a compound partnership and you must weight each capital by its time: share ratio = C₁T₁ : C₂T₂ : … (this product is called the "monthly equivalent capital"). Worked: A puts in ₹15,000 for 12 months, B puts in ₹20,000 for only 6 months. Ratio = (15000 × 12) : (20000 × 6) = 180000 : 120000 = 3 : 2. A profit of ₹25,000 over 5 parts → one part ₹5,000 → A ₹15,000, B ₹10,000. Notice B invested more money and still earned less — because time counts.

When a partner joins late. A starts a shop with ₹20,000. Six months later B joins with ₹30,000. At the end of the year the profit is ₹35,000. A's money worked 12 months, B's only 6. Ratio = (20000 × 12) : (30000 × 6) = 240000 : 180000 = 4 : 3, total 7 parts. One part = 35000/7 = ₹5,000 → A ₹20,000, B ₹15,000.

⚠️ Exam trap
In the example above, the bare capital ratio is 20,000 : 30,000 = 2 : 3, which would give B 3/5 of ₹35,000 = ₹21,000. That is the printed wrong option. The moment a question mentions "after 4 months", "joined later", "withdrew in August", the ratio must be capital × time. Read the months before you touch the rupees.

Working partner and sleeping partner. A partner who also manages the business is a working partner and is usually paid a salary or a commission out of the profit first; only the remainder goes in the capital ratio. A sleeping partner contributes money alone. Worked: A (working) invests ₹60,000 and B (sleeping) ₹90,000. A gets 20% of the profit for managing; the rest is divided in the capital ratio. Total profit = ₹50,000. A's commission = 20% of 50,000 = ₹10,000. Remaining = ₹40,000, split in 60 : 90 = 2 : 3 → A gets 40000 × 2/5 = ₹16,000, B gets 40000 × 3/5 = ₹24,000. So A = 10,000 + 16,000 = ₹26,000 and B = ₹24,000. Check: 26,000 + 24,000 = ₹50,000. ✓

📖 The story
Picture two cousins opening a coaching centre in Patna. One puts in the money and disappears to Delhi; the other puts in half the money but sits at the desk twelve hours a day. Would an equal split feel fair to either of them? That single question is the whole logic of partnership sums: money is weighted by how long it stayed, and labour is paid before profit is divided.

Exam Strategy & the Fraction Shortcuts

With negative marking in the objective paper, the order in which you attempt these questions matters as much as knowing the formulas. Attempt in this order: (1) simple interest — one formula, no traps, 20 seconds; (2) direct profit%, loss% and single-discount questions; (3) compound interest for 2 years and CI−SI difference — mechanical once the formula is memorised; (4) simple partnership. Leave for the end: instalments, three-year CI, false-weight-plus-markup combinations and anything with an unusual base. Never guess a partnership question that mentions months — that is where the printed traps live.

Master formula sheet — the whole chapter on one page
FormulaUse it for
Profit% = (SP − CP)/CP × 100Base is always the CP — never the SP.
SP = CP × (100 ± p)/100CP known, find SP. Plus for profit, minus for loss.
CP = SP × 100/(100 ± p)SP known, find CP. Divide — never subtract.
Discount% = (MP − SP)/MP × 100Base here is the MP, not the CP.
Single equivalent = a + b − ab/100Two successive discounts of a% and b%.
MP = CP × (100 + p)/(100 − d)Marking up to keep profit p% after discount d%.
Loss = (x/10)² %Two articles at the same SP, one +x%, one −x%.
Gain% = error/(true − error) × 100Dishonest shopkeeper using a false weight.
SI = P × R × T/100Rearrange to find R, T or P.
R × T = (n − 1) × 100A sum becoming n times under simple interest.
A = P(1 + R/100)ⁿCompound amount; CI = A − P.
A = P(1 − R/100)ⁿDepreciation and any yearly decline.
CI − SI (2 years) = P(R/100)²The single most asked shortcut of this chapter.
CI − SI (3 years) = P(R/100)² × (300 + R)/100The three-year version of the same idea.
Share ratio = C₁T₁ : C₂T₂Partnership; T equal → plain capital ratio.
Percentage → fraction → the CP : SP ratio it hides
PercentageFractionIf it is the profit%, CP : SP
6.25%1/1616 : 17
8.33%1/1212 : 13
11.11%1/99 : 10
12.5%1/88 : 9
14.28%1/77 : 8
16.66%1/66 : 7
20%1/55 : 6
25%1/44 : 5
33.33%1/33 : 4
50%1/22 : 3

Here is how the table saves you a minute. An article sold for ₹1,800 gives a profit of 12.5%. Find the CP. Since 12.5% = 1/8, the CP : SP ratio is 8 : 9. So CP = 1800 × 8/9 = ₹1,600, profit ₹200 — and 200/1600 is indeed 12.5%. ✓ No division by 112.5 anywhere. The same idea works on the discount side: a discount of 12.5% means MP : SP = 8 : 7, so on an MP of ₹2,400 the price paid is 2400 × 7/8 = ₹2,100 (discount ₹300, which is 300/2400 = 12.5%). ✓

🧠 Profit of 1/n → CP : SP = n : (n + 1)
This one line replaces half the arithmetic in the chapter. A profit of 1/n always means CP : SP = n : (n + 1); a loss of 1/n means CP : SP = n : (n − 1). So 16.66% profit → 6 : 7; 33.33% profit → 3 : 4; 20% loss → 5 : 4. Once you see the numbers as small whole ratios, the answer is a single multiplication and never a decimal.
🎯 Why it matters
Why spend a whole chapter here? Because these questions carry a guaranteed answer. A polity question can be disputed, a current-affairs figure can be outdated, but ₹1,449 at 15% profit will have a cost price of ₹1,260 in every exam of every year. Fifteen minutes of daily practice on these four formula families turns a section people skip into a section that lifts your rank.

Key takeaways

  • Profit% and loss% sit on the CP; discount% sits on the MP. SP = CP(100 ± p)/100 and CP = SP × 100/(100 ± p) — divide, never subtract.
  • Two articles at the same SP, one at +x% and one at −x%, always give a loss of (x/10)²%. For x = 20 that is a 4% loss (CPs ₹1,000 and ₹1,500 against total SP ₹2,400).
  • Successive discounts: a + b − ab/100. So 20% + 10% = 28%, not 30%. To keep profit p% after discount d%, mark up to MP = CP(100 + p)/(100 − d) — CP ₹800 with 25% profit after 20% discount → MP ₹1,250.
  • SI = PRT/100. A sum becomes n times when R × T = (n − 1) × 100; doubling in 8 years means R = 12.5% and four times in 24 years.
  • CI: A = P(1 + R/100)ⁿ. ₹8,000 at 10% for 2 years → ₹9,680, CI ₹1,680 (SI ₹1,600). Half-yearly = halve the rate, double the periods; 10% half-yearly is really 10.25% a year.
  • CI − SI for 2 years = P(R/100)² (₹15,000 at 8% → ₹96); for 3 years = P(R/100)²(300 + R)/100 (₹8,000 at 10% → ₹248). Depreciation uses the same formula with a minus sign.
  • Partnership shares go in capital × time: ₹20,000 for 12 months vs ₹30,000 for 6 months = 4 : 3, so on ₹35,000 profit the shares are ₹20,000 and ₹15,000. A working partner is paid first, then the balance is split by capital.

Practice questions (8)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

  1. An article is bought for ₹450 and sold for ₹540. The profit per cent is:

    1. 15%
    2. 16.66%
    3. 20%
    4. 25%
    Show answer

    Answer: C — 20%

    Profit = 540 − 450 = ₹90. Profit% = (90 ÷ 450) × 100 = 20%. (Dividing by the SP instead gives 90/540 = 16.66% — that is the trap option.)

  2. The marked price of a shirt is ₹1,500 and the shop allows a discount of 12%. The selling price is:

    1. ₹1,260
    2. ₹1,320
    3. ₹1,350
    4. ₹1,380
    Show answer

    Answer: B — ₹1,320

    Discount = 12% of 1500 = ₹180, so SP = 1500 − 180 = ₹1,320. By multiplier: 1500 × 88/100 = ₹1,320.

  3. An article sold for ₹1,449 yields a profit of 15%. Its cost price is:

    1. ₹1,200
    2. ₹1,231.65
    3. ₹1,260
    4. ₹1,290
    Show answer

    Answer: C — ₹1,260

    CP = SP × 100/(100 + p) = 1449 × 100/115 = 144900/115 = ₹1,260. Check: 1260 × 1.15 = ₹1,449. Option 2 (₹1,231.65) comes from wrongly subtracting 15% of the SP.

  4. Consider the following statements:
    1. Profit per cent and loss per cent are always calculated on the cost price.
    2. If a man sells two articles at ₹1,200 each, gaining 20% on one and losing 20% on the other, he neither gains nor loses overall.
    Which is/are correct?

    1. Only 1
    2. Only 2
    3. Both 1 and 2
    4. Neither 1 nor 2
    Show answer

    Answer: A — Only 1

    Statement 1 is correct — the base is always the CP. Statement 2 is wrong: CP of the first = 1200 × 100/120 = ₹1,000 and of the second = 1200 × 100/80 = ₹1,500. Total CP ₹2,500 against total SP ₹2,400, so there is a loss of ₹100 = 4%, which matches the shortcut (x/10)² = (20/10)² = 4% loss.

  5. A sum of money doubles itself in 8 years at simple interest. In how many years will it become four times itself?

    1. 16 years
    2. 20 years
    3. 24 years
    4. 32 years
    Show answer

    Answer: C — 24 years

    Doubling means SI = P, so R × 8 = 100 → R = 12.5%. Becoming four times means SI = 3P, i.e. R × T = 300 → T = 300 ÷ 12.5 = 24 years. Shortcut: under simple interest each extra P takes the same 8 years — 2× in 8, 3× in 16, 4× in 24.

  6. The compound interest on ₹8,000 at 10% per annum for 2 years, compounded annually, is:

    1. ₹1,600
    2. ₹1,660
    3. ₹1,680
    4. ₹1,720
    Show answer

    Answer: C — ₹1,680

    Amount = 8000 × (1.1)² = 8000 × 1.21 = ₹9,680, so CI = 9680 − 8000 = ₹1,680. Year by year: ₹800 in year 1 (amount ₹8,800) and ₹880 in year 2. Simple interest would be only ₹1,600 — the extra ₹80 = P(R/100)² = 8000 × 0.01.

  7. The difference between the compound interest and the simple interest on a certain sum for 2 years at 5% per annum is ₹25. The sum is:

    1. ₹8,000
    2. ₹10,000
    3. ₹12,000
    4. ₹12,500
    Show answer

    Answer: B — ₹10,000

    For 2 years, CI − SI = P(R/100)². So 25 = P × (5/100)² = P × 0.0025 → P = 25 ÷ 0.0025 = ₹10,000. Check: CI = 10000 × 1.1025 − 10000 = ₹1,025; SI = (10000 × 5 × 2)/100 = ₹1,000; difference = ₹25.

  8. A starts a business with ₹20,000. Six months later B joins with ₹30,000. At the end of the year the profit is ₹35,000. Consider:
    1. The profit is shared between A and B in the ratio 4 : 3.
    2. B receives ₹21,000.
    Which is/are correct?

    1. Only 1
    2. Only 2
    3. Both 1 and 2
    4. Neither 1 nor 2
    Show answer

    Answer: A — Only 1

    Ratio = capital × time = (20000 × 12) : (30000 × 6) = 240000 : 180000 = 4 : 3, so statement 1 is correct. Total 7 parts, one part = 35000 ÷ 7 = ₹5,000, so A gets ₹20,000 and B gets ₹15,000 — statement 2 is wrong. ₹21,000 comes from wrongly using the bare capital ratio 2 : 3.