# Extra Curriculum Support

This is a comprehensive educational resource designed to provide students with the tools and guidance necessary to excel. This support system is structured to cater to various aspects of learning, ensuring that students are well-prepared for academic challenges and practical applications of mathematical concepts. Some are the key benefits are mentioned below:

**Comprehensive Learning:** This holistic approach helps students gain a thorough understanding of the subject. Practical Application: The resources encourage students to apply mathematical concepts to real-life scenarios, enhancing their practical understanding and problem-solving skills.

**Critical Thinking and Reasoning:** Value-Based and HOTS questions promote critical thinking and reasoning abilities. These skills are crucial for students to tackle complex problems and make informed decisions.

**Exam Preparedness:** Sample Question Papers and NCERT Exemplar Solutions provide ample practice for exams. They help students familiarize themselves with the exam format and types of questions, reducing exam anxiety.

**Ethical and Moral Development:** Value-Based Questions integrate ethical and moral lessons into the learning process, helping in the overall development of students' character and social responsibility. By incorporating these diverse elements, Enhanced Curriculum Support aims to provide a robust and well-rounded knowledge, preparing students for both academic success and real-world challenges.

## Sample Question Papers

**Sec A**

**1. A fan is listed at ₹ 1500 and a discount of 20% is offered on the list price. What additional discount must be offered to the customer to bring the net price to ₹ 1104 ?**

**(a) 15% (b) 12%**

**(c) 10% (d) 8%**

**2. Assertion (A):** **On ₹ 160000 for one year at the rate of 20% per annum, if the interest is compounded quarterly. Then the compound interest will be ₹ 34481.**

**Reason (R):** **Here P = ₹ 160000, R = 5%, n = 4.**

**(a) Both A and R are true and R is the correct explanation of A.**

**(b) Both A and R are true but R is not the correct explanation of A.**

**(c) A is true but R is false.**

**(d) A is false but R is true.**

**3. State True or False:** **The single discount which is equal to two successive discounts 20% and 10% is 30%.**

**4. The list price of a frock is Rs 220. A discount of 20% is announced on sales. What is the sale price?**

**(a) Rs 122 (b) Rs 154**

**(c) Rs 176 (d) Rs 144**

**5. The difference of compounded and simple interest on any amount at 4% annual rate of interest for 2 years ₹ is 4. Find the principal ?**

**(a) ₹2500 (b) ₹2000**

**(c) ₹2400 (d) ₹2600**

**6. Find C.I. on Rs 20,000 for 3 years at 20% per annum compounded annually.**

**(a) Rs 14,000 (b) Rs 15,000**

**(c) None of these (d) Rs 14,560**

**7. The cost of a vehicle is ₹ 1,75, 000. If its value depreciates at the rate of 20% per annum, then the total depreciation after 3 years was:**

**(a) ₹ 82,500 (b) ₹ 86,400**

**(c) ₹ 85,400 (d) ₹ 84,500**

**8. A football team won 10 matches out of the total number of matches they played. If their win percentage was 40%, then how many matches did they play in all ?**

**(a) 26 (b) 30**

**(c) 25 (d) 20**

**9. A scooter was bought at Rs 42,000. Its value depreciated at the rate of 8% per annum. Find its value after one year.**

**(a) Rs 38,640 (b) Rs 35,640**

**(c) Rs 40,640 (d) None of these**

**10. The price of a TV is Rs 13,000. The sales tax charged on it is at the rate of 12%. Find the amount that Vinod will have to pay if he buys it.**

**(a) Rs 13,560 (b) None of these**

**(c) Rs 14,560 (d) Rs 15,560**

**Sec B**

**1. The marked price of a DVD is ₹4500. A shopkeeper allows two successive discounts of 10% and 5% by the force of a customer. Find the selling price of the customer after two discounts are given.**

**2. A scooter was bought at ₹42,000. Its value depreciated at the rate of 8% per annum. Find its value after one year.**

**3. The population of a place increased to 54,000 in 2003 at a rate of 5% per annum. what would be its population in 2005.**

**4. If Chameli had ₹ 600 left after spending 75% of her money, how much did she have in the beginning?**

**5. The price of a TV is ₹13000. The sales tax charged on it is at the rate of 12%. Find the amount that Vinod will have to pay if he buys it.**

**Sec C**

**1. Given, principal = ₹40000, rate of interest = 8% per annum compounded annually. Find:**

**(i) Interest if period is one year.**

**(ii) Principal for Ilnd year.**

**(iii) Interest for Ilnd year.**

**(iv) Amount if period is two year.**

**2. Raheem runs a readymade garment shop. He mark the garments at such a price that even after allowing a discount of 12.5%, gain a profit of 25%. Find the marked price of a jacket which costs him Rs. 2,100.**

**3. What price should a shopkeeper mark on article that costs him ₹600 to gain 20%, after allowing a discount of 10% ?**

**Sec D**

**1. Simran went to a shop which gives 20% discount the following items during sale.**

**(i) Discount is equal to Marked price - ?**

**(ii) Find the sale price of a dress marked at ₹ 1200 ?**

**(a) ₹ 960 (b) ₹ 1000**

**(c) ₹ 1200 (d) ₹ 900**

**(iii) How much discount she will get on pair of shoes marked at ₹ 750 ?**

**(a) 250 (b) 200**

**(c) 100 (d) 150**

**(iv) Find the sale price of a bag marked at ₹ 2000 ?**

**(a) ₹ 1800 (b) ₹ 400**

**(c) ₹ 1500 (d) ₹ 1600**

**(v) Her total saving in the shopping is ₹ 800.**

**(a) True (b) False**

## Value Based Questions

**Problem 1**

**A group of students decide to reduce the use of plastic in their school by 30%.**

**(1) If the school used 1200 plastic bottles last year, how many bottles should they aim to use this year?**

**(2) How does this initiative show the students' concern for the environment?**

**Problem 2**

**Neha helps her grandparents by managing their finances. Her grandparents receive a pension of Rs. 20,000 per month. Neha helps them invest 15% of it in a savings account that offers 6% annual interest.**

**(1) How much will her grandparents earn from this investment in a year?**

**(2) What value of care and financial planning does Neha display?**

**Problem 3**

**Meena wants to donate to an orphanage. She plans to save 25% of her monthly allowance of Rs. 1600.**

**(1) How much will she save in 6 months?**

**(2) What value does Meena's decision to donate and save demonstrate?**

## HOTS

**Q1**

**A bacteria culture grows at a rate of 10% per hour. After 5 hours, the population is found to be 7,200.**

**(i) What was the initial population of the bacteria ?**

**(ii) How long will it take for the population to triple from its initial value ?**

**(iii) If the bacteria culture starts to decay at 5% per hour after a certain point, how does that affect the future population ?**

**Q2**

**A man wants to invest Rs. 20,000 for 5 years. He has two options:**

**Option A:** **A bank offers him 5% interest, compounded annually.**

**Option B:** **Another bank offers him 7% simple interest.**

**(i) Calculate the total amount he will get under both options after 5 years.**

**(ii) Which option is more beneficial and why?**

**(iii) If the man wishes to invest for 10 years, how does the comparison between the two options change ?**

**Q3**

**A trader mixes two types of rice: one costing Rs. 30 per kg and another costing Rs. 50 per kg. He sells the mixture at Rs. 45 per kg. If he mixes them in the ratio 2:3 :**

**(i) Find the cost price of the mixture.**

**(ii) Calculate the profit or loss percentage.**

**(iii) What would happen to the profit or loss percentage if the selling price was Rs. 40 per kg instead ?**

**Q4**

**A shopkeeper buys two sets of chairs. He sells one set at a profit of 20% and the other at a loss of 15%. The total cost price of the two sets is Rs. 50,000, and the selling price is Rs. 53,000. Find:**

**(i) The cost price of each set.**

**(ii) What would be the profit or loss percentage if both sets were sold at the same price ?**

**(iii) Why do different profit and loss percentages impact overall profit/loss differently ?**

## NCERT Exemplar Solutions

**Answer the below given questions.**

**Questions**

**1. Sita is practicing basket ball. She has managed to score 32 baskets in 35 attempts. What is her success rate in per centage?**

**2. The per cent of pure gold in 14 carat gold is about 58.3%. A 14 carat gold ring weighs 7.6 grams. How many grams of pure gold are in the ring?**

**3. A student used the proportion **

**4. During school hours, Neha finished 73% of her homework and Minakshi completed 5/8 of her homework. Who must finish a greater per cent of homework?**

**5. With the decrease in prices of tea by 15% Tonu, the chaiwallah, was able to buy 2 kg more of tea with the same Rs 45 that he spent each month on buying tea leaves for his chai shop. What was the reduced price of tea? What was the original price of tea?**

**6. A store is having a 25% discount sale. Sheela has a Rs 50 gift voucher and wants to use it to buy a board game marked for Rs 320. She is not sure how to calculate the concession she will get. The sales clerk has suggested two ways to calculate the amount payable.**

**Method 1:** **Subtract Rs 50 from the price and take 25% off the resulting price.**

**Method 2:** **Take 25% off the original price and then subtract Rs 50.**

**(a) Do you think both the methods will give the same result? If not, predict which method will be beneficial for her.**

**(b) For each method, calculate the amount Sheela would have to pay. Show your work.**

**(c) Which method do you think stores actually use? Why?**

**7. Brinda purchased 18 coats at the rate of Rs 1,500 each and sold them at a profit of 6%. If customer is to pay sales tax at the rate of 4%, how much will one coat cost to the customer and what will be the total profit earned by Brinda after selling all coats?**

**8. Ashima sold two coolers for Rs 3,990 each. On selling one cooler she gained 5% and on selling the the other she suffered a loss of 5%. Find her overall gain or loss % in whole transaction.**

**9. Find the difference between Compound Interest and Simple Interest on Rs 45,000 at 12% per annum for 5 years.**

**10. If principal = Rs 1,00,000. rate of interest = 10% compounded half yearly. Find:**

**(i) Interest for 6 months.**

**(ii) Amount after 6 months.**

**(iii) Interest for next 6 months.**

**(iv) Amount after one year.**

**11. In 1975, the consumption of water for human use was about 3850 cu.km/year. It increased to about 6000 cu.km/year in the year 2000. Find the per cent increase in the consumption of water from 1975 to 2000. Also, find the annual per cent increase in consumption (assuming water consumption increases uniformly).**

**State whether the given statements are True/False.**

**Questions**

**1. To calculate the growth of a bacteria if the rate of growth is known, the formula for calculation of amount in compound interest can be used.**

**2. Additional expenses made after buying an article are included in the cost price and are known as Value Added Tax.**

**3. Compound interest is the interest calculated on the previous year’s amount.**

**4. C.P. = M.P. – Discount.**

**5. A man purchased a bicycle for Rs 1,040 and sold it for Rs 800. His gain per cent is 30%.**

**6. Simple interest on a given amount is always less than or equal to the compound interest on the same amount for the same time period and at the same rate of interest per annum.**

**7. Three times a number is 200% increase in the number, then onethird of the same number is 200% decrease in the number.**

**8. If the discount of Rs y is available on the marked price of Rs x, then the discount percent is **

**9. The compound interest on a sum of Rs P for T years at R % per annum compounded annually is given by the formula P(1 + (R/100)).**

**10. In case of gain, S.P. = **

**11. In case of loss, C.P. = **

**Choose the correct option**

**Questions**

**1. Suppose for the principal P, rate R% and time T, the simple interest is S and compound interest is C. Consider the possibilities.**

**(i) C > S (ii) C = S (iii) C < S**

**Then:**

**(a) only (i) is correct.**

**(b) either (i) or (ii) is correct.**

**(c) either (ii) or (iii) is correct.**

**(d) only (iii) is correct.**

**2. Suppose a certain sum doubles in 2 years at r % rate of simple interest per annum or at R% rate of interest per annum compounded annually. We have:**

**(a) r < R (b) R < r**

**(c) R = r (d) can’t be decided**

**3. The compound interest on Rs 50,000 at 4% per annum for 2 years compounded annually is:**

**(a) Rs 4,000 (b) Rs 4,080**

**(c) Rs 4,280 (d) Rs 4,050**

**4. For calculation of interest compounded half yearly, keeping the principal same, which one of the following is true.**

**(a) Double the given annual rate and half the given number of years.**

**(b) Double the given annual rate as well as the given number of years.**

**(c) Half the given annual rate as well as the given number of years.**

**(d) Half the given annual rate and double the given number of years.**

**5. Ashima took a loan of Rs 1,00,000 at 12% p.a. compounded halfyearly. She paid Rs 1,12,360. If **

**(a) 2 years (b) 1 year**

**(c) 6 months (d) 1 12 years**

**6. A bought a tape recorder for Rs 8,000 and sold it to B. B in turn sold it to C, each earning a profit of 20%. Which of the following is true:**

**(a) A and B earn the same profit.**

**(b) A earns more profit than B.**

**(c) A earns less profit than B.**

**(d) Cannot be decided.**

**7. A sum is taken for two years at 16% p.a. If interest is compounded after every three months, the number of times for which interest is charged in 2 years is:**

**(a) 8 (b) 4 (c) 6 (d) 9**

**8. Avinash bought an electric iron for Rs 900 and sold it at a gain of 10%. He sold another electric iron at 5% loss which was bought Rs 1200. On the transaction he has a:**

**(a) Profit of Rs 75 (b) Loss of Rs 75**

**(c) Profit of Rs 30 (d) Loss of Rs 30**

**9. 40% of [100 – 20% of 300] is equal to:**

**(a) 20 (b) 16**

**(c) 140 (d) 64**

**Fill in the blanks**

**Questions**

**(1) ? is charged on the sale of an item by the government and is added to the bill amount.**

**(2) Sales tax = tax % of ?.**

**(3) The time period after which the interest is added each time to form a new principal is called the ?.**

**(4) ? expenses are the additional expenses incurred by a buyer for an item over and above its cost of purchase.**

**(5) The discount on an item for sale is calculated on the ?.**

**(6) When principal P is compounded semi-annually at r % per annum for t years, then Amount = ?.**

**(7) Percentages are ? to fractions with ? equal to 100.**

**(8) ? is a reduction on the marked price of the article.**

**(9) Increase of a number from 150 to 162 is equal to increase of ? per cent.**

**(10) Discount = Discount % of ?.**

## Case Based Questions

**Q1**

**Meera went to the City One shopping complex to buy some return gift items for her son Manvir’s birthday party. She also wanted to buy some personal items for herself and her sister.In the shopping complex, she first enters the Rupee 99 shop, where the price of every item is ₹99.**

**The figure shows a board hung near one of the counters of the Rupee 99 shop where the pencil boxes, which Meera was looking for, were being sold.**

**1. (i) Meera needs to buy 24 pencil boxes. How should she get these 24 items billed to get the maximum discount? Should she get them in sets of 3 + 1 or 5 + 1? Assume Meera would choose one of these two ways of billing, not a combination of these two.**

**(ii) If she gets the maximum possible discount, what is the percentage of money Meera can save compared to the original price, without any discount? Choose the closest percentage value.**

**(a) 20 % (b) 18 % (c) 16 % (d) 14 %**

**(iii) If the shopkeeper decides to display the board by showing the reduced MRP instead of displaying the offer in terms of ‘free’, how much will the price displayed be for one pencil box? (i.e., the selling price for one pencil box). Write your answer in the space provided next to each offer. Round off the answer to the nearest whole number.**

**Buy 5 get 1 free: .......**

**Buy 3 get 1 at 50% off: ......**

**(2) Meera visited City Fancy Shop and selected a nail colour of MRP ₹200 and a purse of MRP₹300, with a discount of 20% and 15%, respectively. While preparing the bill, by mistake, the shopkeeper interchanged the discounts on these items. If Meera pays the amount as per the bill handed over by the shopkeeper, then Meera would pay ........ what she would have paid with the correct calculation.**

**(a) More than**

**(b) Less than**

**(c) Same amount as**

**(3) In her previous visit to the Fashion Jewellery shop, Meera had purchased a fancy earring. She wanted to buy the same one for her sister. But this time its price was increased by 20%. As Meera was a regular customer of this shop, the shopkeeper reduced the price by 20% for her. Meera got the new earrings at ..........**

**(a) more than the original price but less than the current selling price**

**(b) same as the original price**

**(c) less than the original price**

**(4) At the billing counter, Meera saw a board that read, “Shop for ₹1000 and above, get a cosmetic organiser pouch just for ₹49, after 90% o !”. If she wants to calculate the actual cost of a cosmetic organiser, which of the following should she do?**

**(a) Multiply ₹49 with 9**

**(b) Multiply ₹49 with 90**

**(c) Multiply ₹49 with 10**

**(d) Multiply ₹49 with 0.9 and then add ₹4**

**(5) Question 4 talks about a discount of 90% for an item. Do you think it is possible for a seller to give such a discount rate if the marked price was the genuine price of the object?**

**Q2**

**While unwrapping the gift pack of a toy mechanics set that Manvir’s father gifted him for his birthday, the sticker containing the marked price (MP) on the product got torn. But the bill of that product is available. Using the information printed on the bill, answer the following questions regarding the gift.**

**Note: GST in the above bill stands for ‘Goods and Service Tax’. This tax is applied on different products and services. We often notice that one person purchases from one seller and again sells to another customer. E.g., one may purchase plastic beads from one seller and thread from another and ultimately sell a bead necklace to a customer who may further sell it in a jewellery box to another. In such situations, the tax on the plastic beads should be paid only once and not by each seller. The GST system ensures this by making the final seller of the goods and service pay the tax collected from the final buyer.**

**In India, different GST is applicable on different products/services. E.g., the GST on sugar, tea, paneer, etc. is 5% whereas that on mobile phones, ghee, etc. is 12% and it is 28% on items like cars and cement.**

**(1) What is the actual MP of the gift item? Round off the answer to the nearest whole number.**

**(2) Calculate the percentage of GST levied on Manvir’s toy and identify in which slab of GST do toys fall in India. (Recall that GST is always calculated based on the selling price of the item).**

**(a) 5 % (b) 12 % (c) 18 % (d) 28 %**

**(3) We can interpret any bill amount as a price containing a discount in percentage (D%) on its marked price (MP) and an additional tax in percentage (T%) being levied on it. If you want to write a formula for the final bill amount, which of the following can be your choice?**

**Bill Amount = ?**

**(a) **

**(b) **

**(c) **

**(d) **

**Q3**

**1st April is considered to be the beginning of the financial year for the PPF account and 31st March of the next year is the end of the financial year. The interest is compounded annually and the interest money is added to the account at the end of the financial year.**

**Mrs. Harshita opened a PPF account on 2nd April 2020 with an initial deposit of ₹50,000. After 1 year, on 2nd April 2021 she decided to visit the bank to get her passbook updated. On the previous day, she had asked her daughter Sunita to calculate the interest amount. She informs her about the initial deposit of ₹50,000 at an interest rate of 7 % per annum. But she forgets to inform her that the interest is compounded annually.**

**(a) What will be the difference, if any, in the interest amount calculated by Sunita and the one that gets printed in the passbook the next day.**

**(b) What is going to be the balance in Harshita’s account that gets printed in the passbook?**

**(c) For the year 2021-2022, the interest rate was revised and increased to 8%. So, Harshita decided to invest more in the PPF account. She deposited ₹1,20,000/- on 5th April 2021.**

**(i) What is the total principal amount for which Harshita will receive interest at the end of the financial year 2021-2022?**

**(ii) How much would be the interest earned, and what would be the balance in her account at the end of the financial year, i.e., 31st March 2022 ?**

**(d) Mrs. Harshita continues to invest money into her PPF account for 15 years, till she retires. After 15 years, the total amount increases to 40 lakhs. If she stops investing now, what would be the total interest she earns in the next five years? Assume that the interest rate continues to be 8%. Select the option which is closest to the number based on your calculations.**

**(a) ₹ 12,00,000 (b) ₹ 16,00,000**

**(c) ₹ 19,00,000 (d) ₹ 23,00,000**

**Q4**

**We can visualise the difference between “simple interest” and “compound interest” over a period of time through a simple activity of drawing the graphs corresponding to these two quantities. With this activity we can also see the rate at which the interest earned through compounding grows as the number of years increases.**

**For this, you need to assume that a certain principal amount is deposited in the bank for a certain number of years. Calculate the simple interest and the compound interest for successive years, by assuming a fixed interest rate for all the years. Draw the graphs corresponding to these amounts.**

Year | SI earned | CI earned | Year | SI earned | CI earned |
---|---|---|---|---|---|

1 | 9,000 | 9,000 | 9 | 81,000 | 117189 |

2 | 18,000 | 18810 | 10 | 90,000 | 136736 |

3 | 27,000 | 29502 | 11 | 99,000 | 158042 |

4 | 36,000 | 41158 | 12 | 1,08,000 | 181266 |

5 | 45,000 | 53862 | 13 | 1,17,000 | 206580 |

6 | 54,000 | 67710 | 14 | 1,26,000 | 234172 |

7 | 63,000 | 82803 | 15 | 1,35,000 | 264248 |

8 | 72,000 | 99256 |

**The above table shows the total simple interest (SI) earned till the given year and the compound interest (CI) earned till the given year by depositing ₹1,00,000/- for 15 years. For both types of interests, a fixed interest rate is considered for all the years. The above graph shows the bar graph of SI earned and CI earned vs Time.**

**(A) (i) What is the interest rate considered while calculating the interest amount in the table?**

**(a) 10 %**

**(b) 9 %**

**(c) 4.5 %**

**(d) Data is insufficient**

**(ii) In the table, the difference between the interest amount of two successive years ..... as the number of years increases.**

**(a) remains the same in both cases**

**(b) increases in SI earned but decreases in CI earned**

**(c) decreases in SI earned but increases in CI earned**

**(d) remains the same in SI earned but increases in CI earned**

**(iii) As per Table 3.1, which of the following is not the accurate description of the relationship between SI earned and CI earned in 10 years?**

**(a) SI earned is more than 50% of CI earned**

**(b) CI earned is more than 150% of SI earned**

**(c) The difference between the CI earned and SI earned is more than 50% of SI earned**

**(d) The difference between the CI earned and SI earned is more than 50% of CI earned**

**(B) In the graph, instead of plotting only the SI earned and CI earned, if the sum principal + SI earned and principal + CI earned were plotted with the same coloured bars (i.e., orange and green respectively), then which of the following differences would be observed in the graph? (Choose all that apply)**

**(a) For year 13 and above, the green bars would cross 300000**

**(b) Only for year 15, the orange bar would cross 300000**

**(c) For year 9 and above, all the green bars would cross 200000**

**(d) For year 12 and above, all the orange bars would cross 200000**

**(C) As a further exploration, you can extend the table for more years by keeping the same interest rate and plot the graph again. In the below figure, shows a line graph of SI earned and CI earned vs time by extending the table for 30 years.**

**We can see that the CI earned is roughly two times the SI earned in the 16th year. In which year does the CI earned become roughly three times the SI earned?**

**(a) 18th year**

**(b) 23rd year**

**(c) 26th year**

**(d) 28th year**

**(D) Which of the following statements is true about the compound interest earned by the principal amount of ₹1,00,000?**

**I. The compound interest is more than 2 times the principal amount after 10 years**

**II. The compound interest is more than 4 times the principal amount after 20 years**

**III. The compound interest is more than 12 times the principal amount after 30 years**

**(a) Only II**

**(b) I and II**

**(c) II and III**

**(d) I, II and III**