Comparing Quantities Worksheet

Fill in the blanks Type Questions

1. In a T20 cricket match India batted in the 1^st inning and the total runs on the board was 165. Runs scored by top four batsman are as follows:
   
   Numbers in brackets represents the number of balls played.
   The ratio of the runs scored by Gautam Gambhir to the runs scored by rest of the 10 batsmen is __________.
   
   
2. As it started raining in the city, Pankaj bought new windcheaters one for him and one for his son Ankush. As 40 rupees left after buying the windcheater, he bought some snacks as well. Ankush wanted to know the price of the jackets and so looked at the bill. He found that 12% of sales tax was also included in the bill.
   
   
   If Pankaj spent a total of Rs. 2000, then the value of x is __________.
   
   
3. Tanya borrowed Rs. 75,000 from Vikram to invest in shares. Vikram gave her the money with the terms that she returns it within two years and pays 12% interest overall. Then the sum she will have to pay after 2 years is Rs. __________.
   
   Multiple Choice Questions
   
   
4. During the monsoon, heavy rain is typical. A city recorded 143.01 mm rain in just 3 hours which is 90% of the total rain on a particular day. What is the ratio of the rain recorded in 3 hours to the rain recorded in a full day?
   (a) 10 : 11
   (b) 11.1 : 10.43
   (c) 20.43 : 22.7
   (d) 22 : 21
   
   
5. While coming back from a market Kanan kept looking at the dress hanged in store near her tuition as she liked it very much.
   
   The list price of the dress was Rs. 340 however 20% discount was given. But, Kanan has Rs. 51 less and so she couldn’t buy it. What is the minimum discount that must be given on the list price so that she can buy the dress?
   (a) 10%
   (b) 15%
   (c) 28%
   (d) 35%
   
   
6. A manufacturer sells 10 clothes to a dealer for Rs. 40,000. Dealer then sells these 10 clothes to the shopkeeper for Rs. 50,000. If the VAT applied at every stage is 5%, how much tax does the shopkeeper has to pay?
   (a) Rs. 4,000
   (b) Rs. 2,000
   (c) Rs. 2,500
   (d) Rs. 500
   
   
7. Rahul has completed his graduation and his father Suresh wants him to enroll in MBA. Rahul has passed the test and was selected for MBA but Suresh does not have sufficient money to pay the fees. He then borrowed a loan from the bank. The bank provides two types of loans:
   Type A: Where the interest will be calculated on the same principal amount.
   Type B: Where the interest will be calculated on the amount of the previous year.
   State the type of interest that will be beneficial for Suresh along with the reason
   (a) Type A as it is simple interest
   (b) Type B as it is simple interest
   (c) Type A as it is compound interest
   (d) Type B as it is compound interest
   
   
8. Suman needs a new laptop because the old one stopped working. But she is lacking by Rs. 50,000. So, she kept one of her jewellery at the jewellery shop (named “Jewelry”) as collateral for a Rs. 50,000 loan with 15% annual interest.
   
   Time given by the jeweller to pay the money is 2 years. How much would Suman be required to pay at the end of 2 years if simple interest was applied?
   (a) Rs. 50000
   (b) Rs. 55000
   (c) Rs. 60000
   (d) Rs. 65000
   
   
9. Number of pieces cut by a machine increases at the rate of 10% per hour. If we take the initial count as 3000 and use simple interest formula, we can get the number of pieces cut after 5 hours. Which of the following formula can be used to calculate the number of pieces cut after n hours.
   (a) 
   (b) 
   (c) 
   (d) A_n = P_n × R
   
   
10. Madan is highly worried about her daughter's academic progress. As her daughter would pass 12th in the next 3 years, he deposited Rs. 50,000 in the post office for three years in order to secure his daughter's admission to a reputable university. The post office gives him interest at the rate of 7% compound yearly. Use simple interest formula to find the amount he will get after 3 years. If he deposits the amount for n years, which of the following expression would give the amount received at the end of n years?
    (a) 
    (b) 
    (c) 
    (d) A_n = P_n × R
    
    
11. A school which is 500 metre from Nitya’s house don’t have any stationery shop with in 1km. So, her father opens a new stationery shop near his house and to fulfil the cost, he takes a loan of Rs. 126000 from the bank for 2 years at 10% per annum compounded annually. If he pays Rs. 100000 in 1 year, how much more does he need to pay at the end of 2 years?
    (a) Rs. 100000
    (b) Rs. 84040
    (c) Rs. 52460
    (d) Rs. 26000
    
    
12. Number of employees who spent more than 5 years in a company decreases at the rate of 5% per year and number of employees with less than 5 years increases at the rate of 10% per year. The initial counts are as follows:
    
    What is the number of employees after 2 years?
    (a) 108000
    (b) 245000
    (c) 353000
    (d) 390290
    
    
13. Nina did a shopping for the entire month and relooked at the bills. She found that there is a change in price in every item over last 1 year but the change in olive oil’s price is huge compare to other items. If the price increases by 5% every 4 months compare to the previous months, what would be the final price (in nearest integer) after 12 months when the initial price was Rs. 510?
    (a) Rs. 530
    (b) Rs. 550
    (c) Rs. 590
    (d) Rs. 630
    
    Subjective Questions
    
    
14. Harry receives 40 rupees as pocket money each day. He is quite good at managing his money and saves 80% of his income.
    
    He wanted a new comic book with a listed price of Rs. 1000, but he was unable to fulfil his demand within a month. Will a 4% discount allow him to purchase the book in a month? (Take number of days in a month = 30)
    
    
15. Sarah along with her family went to their farmhouse which is located in Goa. They spent a week and then came back. They purchased 10 kg of cashews on their way back, 5 kg for themselves and another 5 kg for Sarah's uncle. 
    
    The total cost of cashews is Rs. 9,200 including a GST of 15%. How much Sarah’s uncle has to pay if GST is not taken?
    
    
16. Akash's parents relocated to his home and will now reside there. They found it challenging to go on a two-wheeler, so Akash purchased a new vehicle. He made a cash payment of 2 lakhs and then borrowed the rest 7 lakhs.
    
    The loan taken for 5 years at 8% interest compounded annually. Which type of interest will be applicable here? Also, clarify whether he will be required to pay the same interest amount if the interest is calculated directly.
    
    
17. Ankit is opening a new shoe shop in the market near his house. He borrowed some cash from her sister Kriti and utilised some of his savings, but he still needs Rs. 1,20,000. He therefore took out a two-year loan from a bank for Rs. 1,20,000 at a cost of 5% per year. Calculate the simple interest to determine how much Ankit will have to pay after two years.
    
    
18. Maya believes she is wasting her money on unnecessary items, so she creates a fixed deposit account for Rs. 1,35,000 for a two-year term in order to save money. The rate of interest offered by the bank are as follows:
    
    Find the sum assured and also, the interest paid by the bank.
    
    
19. As the consumption of junk foods in the new generation people is more compare to old once. While doing a survey Raj found that the consumption of junk food in their building increases by 10% every year. If the initial consumption was 60 kg, what would be the consumption after 5 years?
    
    
20. Sanya's uncle purchased a new phone two years ago and discovered that it functions just as well today as it did then. Sanya looked up the cost because she wanted to purchase the same cell phone. The cost depreciated at an annual rate of 8%. If her uncle purchased the phone for Rs. 45,000, how much will Sanya pay for it?

Fill in the blanks Type Questions

1. In a T20 cricket match India batted in the 1^st inning and the total runs on the board was 165. Runs scored by top four batsman are as follows:
   
   Numbers in brackets represents the number of balls played.
   The ratio of the runs scored by Gautam Gambhir to the runs scored by rest of the 10 batsmen is __________.
   
   Correct Answer: 5 : 6
   Solution: Total score = 165
   Runs scored by Gautam Gambhir = 75
   Runs scored by other batsmen = 165 – 75 = 90
   Ratio of the runs scored by Gautam Gambhir to the runs scored by rest of the 10 batsmen
   = 75 : 90
   = 5 : 6
   
   
2. As it started raining in the city, Pankaj bought new windcheaters one for him and one for his son Ankush. As 40 rupees left after buying the windcheater, he bought some snacks as well. Ankush wanted to know the price of the jackets and so looked at the bill. He found that 12% of sales tax was also included in the bill.
   
   
   If Pankaj spent a total of Rs. 2000, then the value of x is __________.
   
   Correct Answer: 1750
   Solution: Let the price of the windcheaters without tax be Rs. x
   Sales tax = 12% of Rs. x =Rs × x
   Amount spent on windcheaters = Rs. 2000 – Rs. 40 = Rs. 1960
   ⇒ Rs.x+Sales tax=Rs.1960
   ⇒ x + × x = 1960
   ⇒  × x = 1960
   ⇒ x = 
   ⇒ x = 1750
   Hence, the price of the windcheaters without tax is Rs. 1750.
   
   
3. Tanya borrowed Rs. 75,000 from Vikram to invest in shares. Vikram gave her the money with the terms that she returns it within two years and pays 12% interest overall. Then the sum she will have to pay after 2 years is Rs. __________.
   
   Correct Answer: 93000
   Solution: As the interest paid is 12% and it is applied on the principal only once, simple interest is applicable here.
   Interest =  = Rs.18000
   Amount = Principal + Interest
   = Rs. 75000 + Rs. 18000
   = Rs. 93000
   Thus, the sum Tanya will have to pay after 2 years is Rs. 93000.
   
   Multiple Choice Questions
   
   
4. During the monsoon, heavy rain is typical. A city recorded 143.01 mm rain in just 3 hours which is 90% of the total rain on a particular day. What is the ratio of the rain recorded in 3 hours to the rain recorded in a full day?
   (a) 10 : 11
   (b) 11.1 : 10.43
   (c) 20.43 : 22.7
   (d) 22 : 21
   
   Correct Option: (c) 20.43 : 22.7
   Solution: Let x mm rain recorded in a full day.
   90% of x is 143.01 mm
   ⇒ ×x = 143.01
   ⇒ x = 
   ⇒ x = 158.9
   So, 158.9 mm rain recorded in a full day.
   ∴ Ratio of the rain recorded in 3 hours to the rain recorded in a full day
   = 
   = 
   
   
5. While coming back from a market Kanan kept looking at the dress hanged in store near her tuition as she liked it very much.
   
   The list price of the dress was Rs. 340 however 20% discount was given. But, Kanan has Rs. 51 less and so she couldn’t buy it. What is the minimum discount that must be given on the list price so that she can buy the dress?
   (a) 10%
   (b) 15%
   (c) 28%
   (d) 35%
   
   Correct Option: (d) 35%
   Solution: Marked price of the dress = Rs. 340
   Discount = 20% of Rs. 340 = Rs.× 340 = Rs.68
   ⇒ Sale price of the dress = Rs. 340 – Rs. 68 = Rs. 272
   Kanan has Rs. 51 less than the sale price of the dress.
   Discount of Rs. 51 more must be given.
   Total discount = Rs. 68 + Rs. 51 = Rs. 119
   Let the discount of x% is given on the list price so that Kanan can buy the dress.
   ⇒ x% of Rs.340 = Rs.119
   ⇒ × 340 = 119
   ⇒ x = 
   ⇒ x = 35
   Hence, the minimum discount that must be given on the list price is 35%.
   
   
6. A manufacturer sells 10 clothes to a dealer for Rs. 40,000. Dealer then sells these 10 clothes to the shopkeeper for Rs. 50,000. If the VAT applied at every stage is 5%, how much tax does the shopkeeper has to pay?
   (a) Rs. 4,000
   (b) Rs. 2,000
   (c) Rs. 2,500
   (d) Rs. 500
   
   Correct Option: (c) Rs. 2500
   Solution: For the manufacture:
   Tax collected by the manufacturer = 5% of Rs. 40,000 
   =  × 40000 = Rs.2000
   ⇒ Tax paid by the dealer to the manufacturer = Rs. 2000
   Manufacturer pays Rs. 2000 to the government.
   Tax collected by the dealer from the shopkeeper = 5% of Rs. 50,000 
   = × 50000 = Rs.2500
   Dealer will then pay Rs. 500 to the government as Rs. 2000 is paid by the manufacture.
   So, the shopkeeper has to pay a tax of Rs. 2500.
   
   
7. Rahul has completed his graduation and his father Suresh wants him to enroll in MBA. Rahul has passed the test and was selected for MBA but Suresh does not have sufficient money to pay the fees. He then borrowed a loan from the bank. The bank provides two types of loans:
   Type A: Where the interest will be calculated on the same principal amount.
   Type B: Where the interest will be calculated on the amount of the previous year.
   State the type of interest that will be beneficial for Suresh along with the reason
   (a) Type A as it is simple interest
   (b) Type B as it is simple interest
   (c) Type A as it is compound interest
   (d) Type B as it is compound interest
   
   Correct Option: (a) Type A as it is simple interest
   Solution: When the interest in calculated on the entire amount only once, it is less than the interest calculated 
   multiple times on the amount of the previous year.
   Interest given in Type A is simple interest
   Interest given in Type B is compound interest
   So, when one has to pay the interest, simple interest is beneficial as it is less compare to compound interest.
   Hence, Type A is beneficial for Suresh as it is simple interest.
   
   
8. Suman needs a new laptop because the old one stopped working. But she is lacking by Rs. 50,000. So, she kept one of her jewellery at the jewellery shop (named “Jewelry”) as collateral for a Rs. 50,000 loan with 15% annual interest.
   
   Time given by the jeweller to pay the money is 2 years. How much would Suman be required to pay at the end of 2 years if simple interest was applied?
   (a) Rs. 50000
   (b) Rs. 55000
   (c) Rs. 60000
   (d) Rs. 65000
   
   Correct Option: (d) Rs. 65000
   Solution: Suman takes a loan of Rs. 50,000 at the rate on interest 15% per annum for 2 years.
   ⇒ Principal = Rs. 50000, time = 2 years and rate of interest = 15%
   Interest =  =Rs.15000
   Amount to be paid by Suman = Principal + Interest 
   = Rs. 50000 + Rs. 15000 
   = Rs. 65000
   
   
9. Number of pieces cut by a machine increases at the rate of 10% per hour. If we take the initial count as 3000 and use simple interest formula, we can get the number of pieces cut after 5 hours. Which of the following formula can be used to calculate the number of pieces cut after n hours.
   (a) 
   (b) 
   (c) 
   (d) A_n = P_n × R
   
   Correct Option: (a) 
   Solution: Take the initial count as Principal (P₁) = 3000
   Number of pieces increased after 1 hour =  =300
   After 1 hour, the number of pieces increases by 10% and that becomes the new principal.
   Amount (A₁) = 3000 + 300 = 3300 = Principal (P2)
   Number of pieces increased after 2 hours =  =330
   Amount (A₂) = P₂ + 330 = 3630 = Principal (P3)
   Number of pieces increased after 3 hours = =363
   Amount (A3) = 3630 + 363 = 3993
   SI₁ = =300
   Let’s find the formula:
   A₁ = P₁ + SI₁ = 3000 + 
   
   
   
   
   
   
   So, the formula to calculate the number of pieces cut after n hours is given by:
   
   
   
10. Madan is highly worried about her daughter's academic progress. As her daughter would pass 12th in the next 3 years, he deposited Rs. 50,000 in the post office for three years in order to secure his daughter's admission to a reputable university. The post office gives him interest at the rate of 7% compound yearly. Use simple interest formula to find the amount he will get after 3 years. If he deposits the amount for n years, which of the following expression would give the amount received at the end of n years?
    (a) 
    (b) 
    (c) 
    (d) A_n = P_n × R
    
    Correct Option: (a) 
    Solution: The initial deposit amount is Principal (P1) = Rs. 50000
    Interest for 1^st  year (SI₁) = =Rs.3500
    Amount (A₁) = 50000 + 3500 = Rs. 53500 = Principal (P₂)
    Interest for 2^nd  year (SI₂) = =Rs.3745
    Amount (A₂) = 53500 + 3745 = 57245 = Principal (P₃)
    Interest for 3^rd year (SI₃ ) = =Rs.4007.15
    Amount (A₃) = 57245 + 4007.15 = 61252.15
    Let’s find the formula:
    
    
    
    
    
    
    
    
    So, the formula to calculate the number of pieces cut after n hours is given by:
    
    
    
11. A school which is 500 metre from Nitya’s house don’t have any stationery shop with in 1km. So, her father opens a new stationery shop near his house and to fulfil the cost, he takes a loan of Rs. 126000 from the bank for 2 years at 10% per annum compounded annually. If he pays Rs. 100000 in 1 year, how much more does he need to pay at the end of 2 years?
    (a) Rs. 100000
    (b) Rs. 84040
    (c) Rs. 52460
    (d) Rs. 26000
    
    Correct Option: (c) Rs. 52460
    Solution: As the interest is compounded, so compound interest can be applied here.
    Here, Principal (P) = Rs. 126000, Rate of interest (R) = 10% and Time (n) = 2 years
    
    
    
    =Rs.152460
    As he already paid Rs. 100000 in 1 year, he needs to pay Rs. 52460 more at the end of 2 years.
    
    
12. Number of employees who spent more than 5 years in a company decreases at the rate of 5% per year and number of employees with less than 5 years increases at the rate of 10% per year. The initial counts are as follows:
    
    What is the number of employees after 2 years?
    (a) 108000
    (b) 245000
    (c) 353000
    (d) 390290
    
    Correct Option: (d) 390290
    Solution: As the number of employees spent more than 5 years decreases at the rate of 5% per year.
    So, this forms a compound interest where the rate of interest is –5%.
    Also, as the number of employees with less than 5 years increases at the rate of 10% per year.
    So, this also forms a compound interest with rate interest 10%.
    Number of employees who spent more than 5 years after two years
    
    
    
    =97470
    Number of employees who spent less than 5 years after two years
    
    =24500
    
    =292820
    Total number of employees = 97470 + 292820 = 390290
    
    
13. Nina did a shopping for the entire month and relooked at the bills. She found that there is a change in price in every item over last 1 year but the change in olive oil’s price is huge compare to other items. If the price increases by 5% every 4 months compare to the previous months, what would be the final price (in nearest integer) after 12 months when the initial price was Rs. 510?
    (a) Rs. 530
    (b) Rs. 550
    (c) Rs. 590
    (d) Rs. 630
    
    Correct Option: (c) Rs. 590
    Solution: As the price increases by 3% every 4 months compare to the previous months.
    So, compound interest is applicable in this case.
    Initial price becomes the principal i.e. P = Rs. 510
    Rate of interest (R) = 5% and Time (n) = 12 months = 3 four months
    
    
    
    = Rs.590.38
    Hence, the final price after 12 months is Rs. 590.38.
    The nearest integer is 590 and so the final price is Rs. 590.
    
    Subjective Questions
    
    
14. Harry receives 40 rupees as pocket money each day. He is quite good at managing his money and saves 80% of his income.
    
    He wanted a new comic book with a listed price of Rs. 1000, but he was unable to fulfil his demand within a month. Will a 4% discount allow him to purchase the book in a month? (Take number of days in a month = 30)
    
    Solution:
    Harry receives 40 rupees each day and save 80% of it.
    80% of Rs.40 = Rs. × 40 = Rs.32
    Harry’s monthly savings = Rs. 30 × 32 = Rs. 960
    Marked price of the book = Rs. 1000
    4% of Rs.1000 = Rs.× 1000 = Rs.40
    When a discount of 4% is given, sale price of the book = Rs. 1000 – Rs. 40 = Rs. 960
    So, Harry will be able to buy the book when a discount of 4% is given.
    
    
15. Sarah along with her family went to their farmhouse which is located in Goa. They spent a week and then came back. They purchased 10 kg of cashews on their way back, 5 kg for themselves and another 5 kg for Sarah's uncle. 
    
    The total cost of cashews is Rs. 9,200 including a GST of 15%. How much Sarah’s uncle has to pay if GST is not taken?
    
    Solution:
    
    Let Sarah’s uncle pay Rs. x
    Cost of cashews without GST = Rs. 2x
    GST = 15% of 2x = ×2x
    Total cost of cashews = Rs. 9,200
    ⇒ Rs.2x+GST=Rs.9,200
    ⇒ 2x+  ×2x = 9200
    ⇒ 2x  = 9200
    ⇒ 2x  =9200
    ⇒ 2x= 
    ⇒ 2x=8000
    ⇒ x = 4000
    So, Sarah’s uncle has to pay Rs. 4000.
    
    
16. Akash's parents relocated to his home and will now reside there. They found it challenging to go on a two-wheeler, so Akash purchased a new vehicle. He made a cash payment of 2 lakhs and then borrowed the rest 7 lakhs.
    
    The loan taken for 5 years at 8% interest compounded annually. Which type of interest will be applicable here? Also, clarify whether he will be required to pay the same interest amount if the interest is calculated directly.
    
    Solution:
    As it is given that the interest must be compounded annually.
    So, compound interest must be applicable here.
    When the interest is calculated on the amount of previous year, it is more than that of calculated with the same amount every year.
    Hence, if the interest is calculated directly, Akash will have to a different interest amount compare to what he paid earlier.
    
    
17. Ankit is opening a new shoe shop in the market near his house. He borrowed some cash from her sister Kriti and utilised some of his savings, but he still needs Rs. 1,20,000. He therefore took out a two-year loan from a bank for Rs. 1,20,000 at a cost of 5% per year. Calculate the simple interest to determine how much Ankit will have to pay after two years.
    
    Solution:
    Here, Principal = Rs. 120000, Time = 2 years, Rate of interest = 5%
    Simple Interest =  =Rs.12000
    Amount = Principal + Interest
    = Rs. 120000 + Rs. 12000
    = Rs. 132000
    So, Ankit has to pay Rs. 132000.
    
    
18. Maya believes she is wasting her money on unnecessary items, so she creates a fixed deposit account for Rs. 1,35,000 for a two-year term in order to save money. The rate of interest offered by the bank are as follows:
    
    Find the sum assured and also, the interest paid by the bank.
    
    Solution:
    Whenever the interest is paid by the bank, it is paid yearly on the basis of the amount of the previous year.
    So, here the interest is compounded annually and hence the compound interest can be used.
    Given: Principal (P) = Rs. 135000
    As Maya deposit the amount for 2 years, we have
    Rate of interest = 7.00% and Time (n) = 2 years.
    Using compound interest formula, we have
    
    
    
    
    = Rs.154561.5
    Interest offered = A – P = Rs. 19,561.5
    Hence, the sum assured = Rs. 154561.5 and interest offered = Rs. 19,561.5.
    
    
19. As the consumption of junk foods in the new generation people is more compare to old once. While doing a survey Raj found that the consumption of junk food in their building increases by 10% every year. If the initial consumption was 60 kg, what would be the consumption after 5 years?
    
    Solution:
    As the consumption of junk food in a building increases by 10% every year, so compound interest is applied in this case.
    Here, principal (P) = 60, Rate of interest (R) = 10% and Time (n) = 5
    
    
    
    =96.63
    So, the consumption of junk foods after 5 years would be 96.63 kg.
    
    
20. Sanya's uncle purchased a new phone two years ago and discovered that it functions just as well today as it did then. Sanya looked up the cost because she wanted to purchase the same cell phone. The cost depreciated at an annual rate of 8%. If her uncle purchased the phone for Rs. 45,000, how much will Sanya pay for it?
    
    Solution:
    As the cost of the mobile phone was depreciated at the rate of 8% per annum.
    So, compound interest is applicable here with the rate of interest –8%.
    Cost of mobile after 2 years
    
    = 45000 × 
    
    = Rs.38088
    Thus, Sanya has to pay Rs. 38088.