CBSE
Madhu and Kavitha's House: Class 8 Profit and Loss Word Problems Solved
Madhu and Kavitha bought the house for Rs 3,20,000 and sold it for Rs 2,80,000, so the loss is 320000 - 280000 = Rs 40,000. Loss percent = (40000/320000) × 100 = 12.5 percent, because loss percent is always calculated on the cost price, never the selling price.
If you searched for Madhu and Kavitha, you almost certainly have a Class 8 Comparing Quantities exercise open in front of you. The standard version of the question uses Rs 3,20,000 as the purchase price and Rs 2,80,000 as the selling price, and the whole thing rests on two formulas: loss = CP - SP, and loss percent = (loss/CP) × 100. The question is paraphrased below, since the original wording is copyrighted, and solved the way CBSE examiners like to see it: given, formula, substitution, answer with units. After it come five more profit, loss and discount problems of the same type, each with a fresh variant for you to try.
The three formulas that run all of Chapter 8
Cost price (CP) is what the seller paid; selling price (SP) is what the buyer pays. If SP is bigger you have a profit, SP - CP. If CP is bigger you have a loss, CP - SP. Percentages are always taken on the cost price: profit percent = (profit/CP) × 100 and loss percent = (loss/CP) × 100. Discount is the odd one out. It is a reduction on the marked price, the number printed on the tag, so discount = (discount percent/100) × marked price, and what the customer pays is marked price minus discount. Every question on this page, including Madhu and Kavitha, is one of these three moves or two of them chained together. If you read a question and cannot name which formula it wants, underline the numbers and label each one CP, SP, MP or percent before you touch your calculator.
Where the Madhu and Kavitha question comes from
This question circulates with Class 8 Comparing Quantities practice sets, and the version everyone searches uses Rs 3,20,000 as the purchase price and Rs 2,80,000 as the sale price, which is why those are the numbers solved above. Some guidebooks change the figures, and that is fine, because the numbers are not the point. The structure is: two people buy an asset, circumstances force a sale below cost, find the loss and the loss percent. Swap the house for a shop, a plot or a car and the method is identical: subtract to get the loss, divide by the cost price, multiply by 100. If your textbook's version shows different amounts, run the same three steps with your numbers and you will land on the right answer.
Setting out a full-marks answer
CBSE maths marking rewards visible structure. For a 3-mark word problem the split is typically one mark for correctly identifying what is given and the formula, one for the substitution and arithmetic, and one for the final answer with units and a closing statement. So write: Given, with the values labelled CP and SP; the formula before any numbers; the substitution on its own line; and a sentence at the end like therefore the loss percent is 12.5 percent. Two habits cost marks repeatedly: doing the subtraction mentally so the examiner cannot see where 40,000 came from, and leaving a bare number without Rs or percent. Neither habit saves real time. Written out properly, the Madhu and Kavitha solution is six short lines.
Worked questions, step by step
Madhu and Kavitha bought a new house together for Rs 3,20,000. Money troubles later forced them to sell it, and the buyer paid Rs 2,80,000. Work out (i) how much money they lost and (ii) the loss percent.
- Given: cost price CP = Rs 3,20,000 and selling price SP = Rs 2,80,000. To find: the loss and the loss percent.
- Since SP is less than CP, this is a loss. Formula: Loss = CP - SP.
- Loss = 320000 - 280000 = Rs 40,000.
- Formula for the percentage: Loss percent = (Loss/CP) × 100, always taken on the cost price.
- Loss percent = (40000/320000) × 100 = (1/8) × 100 = 12.5 percent.
- Answer: they lost Rs 40,000, which is a loss of 12.5 percent.
Answer: Loss = Rs 40,000; loss percent = 12.5 percent
Where marks slip: The classic slip here is dividing by the selling price 2,80,000 instead of the cost price, which gives about 14.3 percent and loses the accuracy mark, so anchor the percent to CP every time.
Try one yourself: Two sisters bought a shop for Rs 4,50,000 and had to sell it for Rs 4,05,000. Find the loss and the loss percent. (Answer: Rs 45,000 and 10 percent)
A stationery shop owner buys 80 notebooks at Rs 12 each and manages to sell every one of them at Rs 15 each. Find the total profit and the profit percent.
- Given: 80 notebooks, cost Rs 12 each, sold at Rs 15 each. To find: profit and profit percent.
- Total CP = 80 × 12 = Rs 960 and total SP = 80 × 15 = Rs 1,200.
- Formula: Profit = SP - CP, so profit = 1200 - 960 = Rs 240.
- Profit percent = (240/960) × 100 = 25 percent, calculated on the cost price.
- Answer: profit Rs 240 and profit percent 25 percent.
Answer: Profit = Rs 240; profit percent = 25 percent
Where marks slip: Students often use the per-notebook prices for the profit but the totals for the percent, or the other way round; either route gives 25 percent, but mixing them mid-solution is where the arithmetic goes wrong.
Try one yourself: A fruit seller buys 50 melons at Rs 8 each and sells them all at Rs 9 each. Find her profit percent. (Answer: 12.5 percent)
Ravi paid Rs 2,400 for a second-hand bicycle. After a few months he sold it at a loss of 15 percent. What price did he sell it for?
- Given: CP = Rs 2,400 and loss = 15 percent of CP. To find: the selling price.
- Formula: SP = CP × (100 - loss percent)/100.
- SP = 2400 × 85/100 = 2400 × 0.85.
- SP = Rs 2,040.
- Answer: Ravi sold the bicycle for Rs 2,040.
Answer: Selling price = Rs 2,040
Where marks slip: Working out 15 percent of 2,400 and then forgetting to subtract it from the cost price is the usual error, so either use the 85/100 multiplier in one move or clearly show the subtraction 2400 - 360.
Try one yourself: Ayesha bought a study table for Rs 3,600 and sold it at a 10 percent loss. Find the selling price. (Answer: Rs 3,240)
A trader sells a watch for Rs 1,725 and makes a profit of 15 percent on it. How much had the watch cost him?
- Given: SP = Rs 1,725 and profit = 15 percent. To find: the cost price.
- Formula: SP = CP × (100 + profit percent)/100, so CP = SP × 100/115.
- CP = 1725 × 100/115 = 172500/115 = Rs 1,500.
- Check: 15 percent of 1500 is 225, and 1500 + 225 = 1725, which matches the given SP.
- Answer: the watch cost the trader Rs 1,500.
Answer: Cost price = Rs 1,500
Where marks slip: Taking 15 percent of the selling price and subtracting it (1725 - 258.75) is the trap; the 15 percent is defined on the unknown CP, so you must divide by 115/100 rather than subtract.
Try one yourself: A dealer sold a chair for Rs 2,760 at a profit of 20 percent. Find the cost price. (Answer: Rs 2,300)
A winter jacket has a price tag of Rs 1,850, and the store is running a 20 percent discount on it. Find the discount in rupees and the price a customer actually pays.
- Given: marked price MP = Rs 1,850 and discount = 20 percent. To find: the discount amount and the sale price.
- Formula: Discount = (discount percent/100) × MP, taken on the marked price, not the cost price.
- Discount = (20/100) × 1850 = Rs 370.
- Sale price = MP - discount = 1850 - 370 = Rs 1,480.
- Answer: the discount is Rs 370 and the customer pays Rs 1,480.
Answer: Discount = Rs 370; sale price = Rs 1,480
Where marks slip: Discount always comes off the marked price, so if you catch yourself using CP anywhere in a pure discount question, stop and reread it, because that mix-up costs the whole method mark.
Try one yourself: A school bag marked at Rs 2,400 carries a 15 percent discount. What does the buyer pay? (Answer: Rs 2,040)
A shop marks a pair of shoes at Rs 900 and offers a 10 percent discount on the tag. Even after the discount, the shopkeeper makes a 12.5 percent profit. What was the cost price of the shoes?
- Given: MP = Rs 900, discount = 10 percent, profit after discount = 12.5 percent. To find: the cost price.
- First find the actual selling price: SP = 900 × (100 - 10)/100 = 900 × 90/100 = Rs 810.
- The profit percent connects SP and CP: SP = CP × (100 + 12.5)/100 = CP × 112.5/100.
- So CP = 810 × 100/112.5 = 81000/112.5 = Rs 720.
- Check: 12.5 percent of 720 is 90, and 720 + 90 = 810, which matches the discounted price.
- Answer: the shoes cost the shopkeeper Rs 720.
Answer: Cost price = Rs 720
Where marks slip: This is a two-stage question and the marks are split that way: one for getting SP = Rs 810 from the marked price, and the rest for connecting SP to CP, so never try to jump from 900 straight to CP.
Try one yourself: A kettle is marked Rs 600 and sold at a 5 percent discount, still giving the seller a 14 percent profit. Find the cost price. (Answer: Rs 500)
Stuck on a different question?
Paste or photograph it and get the full working, free — no account needed.
Solve my question →Quiz me on this topicQuestions students ask
What is the answer to the Madhu and Kavitha house question?
In the standard version, the house is bought for Rs 3,20,000 and sold for Rs 2,80,000. The loss is 320000 - 280000 = Rs 40,000, and the loss percent is (40000/320000) × 100 = 12.5 percent. If your book uses different figures, apply the same two steps: subtract for the loss, then divide by the cost price and multiply by 100.
Is loss percent calculated on the cost price or the selling price?
On the cost price, always, unless a question explicitly says otherwise. Profit and loss are measured against what the seller originally invested, so the denominator is CP. Dividing by SP gives a different number, about 14.3 percent in the house problem instead of 12.5, and it will be marked wrong even though the subtraction step was fine.
What is the difference between a discount and a loss?
A discount is a reduction on the marked price, the tag price a shop displays, and it may still leave the seller in profit. A loss compares selling price with cost price, what the seller actually paid. A question can involve both at once: problem 6 above discounts a Rs 900 tag to Rs 810 while the shopkeeper still earns 12.5 percent profit on a Rs 720 cost.
How should I set out profit and loss answers in the exam?
Use the pattern in the solutions above: state what is given with labels CP, SP or MP, write the formula before substituting, show the substitution as its own line, and finish with the answer carrying units, Rs or percent, plus a short closing statement. Markers award the formula, the working and the final statement separately, so each visible line protects a mark.