Comparing Quantities Worksheet

      Multiple Choice Questions

1. Consider two numbers P and Q. When these two numbers are added, the sum is equal to  of number P. What percent is number Q of number P?
   (a) 
   (b)
   (c) 60%
   (d) 30%
   
   
2. Vanika purchased an umbrella and saved Rs. 120 with discount of 25%. What is the original price of an umbrella?
   
   (a) Rs. 480
   (b) Rs. 145
   (c) Rs. 450
   (d) Rs. 185
   
   
3. Mr. Raghav invested Rs. 15,000 in a bank at a particular rate of simple interest. After 5 years, he received Rs. 23,250 including interest. At what rate of interest he invested his money?
   
   (a) 12%
   (b) 11%
   (c) 10%
   (d) 9%
   
   
4. A ticket to visit museum costs Rs. 440. But the cost of ticket for school students is Rs. 330. What is the percentage of discount for students?
   (a) 10%
   (b) 15%
   (c) 20%
   (d) 25%
   
   
5. If 6% of 200:11% of 100 = k + 1:k, then find the sum of digits of k.
   (a) 2
   (b) 3
   (c) 10
   (d) 11
   
   
6. A jar contains 50 almonds. If Raavi eats 2 almonds daily, what percent of almonds would be eaten by Raavi in 10 days?
   
   (a) 40%
   (b) 50%
   (c) 60%
   (d) 70%
   
   Subjective Questions
   
   
7. Mr. Malhotra’s monthly income, expenses and savings are depicted in the below picture. If entertainment expenses are converted into savings, find the amount saved by Mr. Malhotra.
   
   
   
8. Find the value of 10% of greatest 2-digit even number.
   
   
9. The cost price and selling price of two flowers bouquets are given below.
   
   
   Which bouquet will yield more profit? By how much percent?
   
   
10. In a cupboard, there are 100 clothes in which the ratio of shirts and kurtis is 2 : 3. If 20% of shirts and 10% of kurtis are ironed, find the percentage of clothes which are not ironed.
    
    
11. Identify the boxes equal to ‘2 hundredth’. 
    
    
    
12. Find the percentage of shaded boxes from the below figure.
    
    
    
13. Swati makes rice by adding 3 cups of water to 2 cups of rice. Represent each of the ingredients used in rice as percentage.
    
    
14. For buying a flat on rent, Pooja had to put down a deposit of  of the value of the flat. What percentage was this?
    
    
15. In 2022, the price of bicycle was Rs. 5400. If the price has been increased by 21% this year, find its price this year.
    
    
    
16. Calculate the time in which the simple interest on Rs. 4000 at the rate of 5% per annum will be same as simple interest on Rs. 5000 at 8% per annum for 3 years.
    
    
17. Write the shaded and unshaded parts in the below figure in the form of fraction, percentage and decimal.
    
    
    
18. A tank A of capacity 70 litres is filled with water. For cleaning purpose, 30% of it is used and the remaining water was poured in another tank B of capacity 50 litres. How much percent of tank B is filled with water?
    
    
    
19. Consider numbers 31 to 60. Find the percentage of numbers having digit 9 in the unit’s place.
    
    
20. Samidha distributed 37% of her bonus salary to Ashrams, 33% to Hospitals and the remaining Rs. 12000 she kept for her mother. Find the amount given to Ashrams and Hospitals.

      Multiple Choice Questions

1. Consider two numbers P and Q. When these two numbers are added, the sum is equal to  of number P. What percent is number Q of number P?
   (a) 
   (b) 
   (c) 60%
   (d) 30%
   Correct Option: (c) 60% 
   Solution:
   
   
   
2. Vanika purchased an umbrella and saved Rs. 120 with discount of 25%. What is the original price of an umbrella?
   
   (a) Rs. 480
   (b) Rs. 145
   (c) Rs. 450
   (d) Rs. 185
   Correct Option: (a) Rs. 480
   Solution:
   Let the original price of an umbrella be Rs. x.
   Then,
   
   ⇒x=480
   
   
3. Mr. Raghav invested Rs. 15,000 in a bank at a particular rate of simple interest. After 5 years, he received Rs. 23,250 including interest. At what rate of interest he invested his money?
   
   (a) 12%
   (b) 11%
   (c) 10%
   (d) 9%
   Correct Option: (b) 11%
   Solution:
   Principal, P = Rs. 15000
   Time, T = 4 years
   Interest = Amount – Principal = Rs. (23250 – 15000) = Rs. 8250
   
   
   
4. A ticket to visit museum costs Rs. 440. But the cost of ticket for school students is Rs. 330. What is the percentage of discount for students?
   (a) 10%
   (b) 15%
   (c) 20%
   (d) 25%
   Correct Option: (d) 25%
   Solution:
   Original price of a ticket = Rs. 440
   Discounted price = Rs. 330
    Discount = Rs. (440 – 330) = Rs. 110
   And, discount 
   
   
5. If 6% of 200:11% of 100 = k + 1:k, then find the sum of digits of k.
   (a) 2
   (b) 3
   (c) 10
   (d) 11
   Correct Option: (a) 2
   Solution:
   
   ⇒ 12k = 11k + 11
   ⇒ k = 11
   ⇒ Sum of digits = 1 + 1 = 2
   
   
6. A jar contains 50 almonds. If Raavi eats 2 almonds daily, what percent of almonds would be eaten by Raavi in 10 days?
   
   (a) 40%
   (b) 50%
   (c) 60%
   (d) 70%
   Correct Option: (C) 60%
   Solution:
   Number of almonds in a jar = 50
   Number of almonds eaten by Raavi in a day = 2
   ⇒ Number of almonds eaten by Raavi in 10 days = 3 × 10 = 30
   Therefore, percentage of almonds eaten by Raavi in 10 days 
   Subjective Questions
   
   
7. Mr. Malhotra’s monthly income, expenses and savings are depicted in the below picture. If entertainment expenses are converted into savings, find the amount saved by Mr. Malhotra.
   
   Solution:
   If entertainment expenses are converted into savings, then
   Savings % = 15% + 5% = 20%
    
   
   
8. Find the value of 10% of greatest 2-digit even number.
   Solution:
   Greatest 2-digit even number = 98
   Required value 
   
   
9. The cost price and selling price of two flowers bouquets are given below.
   
   
   Which bouquet will yield more profit? By how much percent?
   Solution:
   For Bouquet I,
   Profit = SP – CP = Rs. (350 – 300) = Rs. 50
   Profit 
   For Bouquet II,
   Profit = SP – CP = Rs. (780 – 700) = Rs. 80
   Profit 
   ⇒ Profit% for bouquet I > Profit% for bouquet II
   Therefore, bouquet I yields more profit than bouquet II.
   
   
10. In a cupboard, there are 100 clothes in which the ratio of shirts and kurtis is 2 : 3. If 20% of shirts and 10% of kurtis are ironed, find the percentage of clothes which are not ironed.
    Solution:
    Let the number of shirts and kurtis in a cupboard be 2x and 3x respectively.
    Then, 2x + 3x = 100
    ⇒ 5x = 100
    ⇒ x = 20
    Then, number of shirts = 2x = 2 × 20 = 40
    And, number of kurtis = 3x = 3 × 20 = 60
    Number of shirts which are ironed 
    Number of kurtis which are ironed 
    So, number of clothes which are not ironed = 100 – 8 – 6 = 86
    And, percentage of clothes which are not ironed
    
    
11. Identify the boxes equal to ‘2 hundredth’. 
    
    Solution:
    
    2 hundredth 
    
    
12. Find the percentage of shaded boxes from the below figure.
    
    Solution:
    Total number of boxes = 10
    Number of shaded boxes = 3
    Therefore, percentage of shaded boxes
    
    
13. Swati makes rice by adding 3 cups of water to 2 cups of rice. Represent each of the ingredients used in rice as percentage.
    Solution:
    Water: Rice = 3:2
    Now, the total number of parts = 3 + 2 = 5
    Then,
    Percentage of water
    Percentage of rice 
    
    
14. For buying a flat on rent, Pooja had to put down a deposit of   of the value of the flat. What percentage was this?
    Solution:
    
    
    
15. In 2022, the price of bicycle was Rs. 5400. If the price has been increased by 21% this year, find its price this year.
    
    Solution:
    Price of bicycle in 2022 = Rs. 5400
    Increased price = Rs. 5400 + 21% of Rs. 5400
    
    = Rs. 5400 + Rs. 1134
    = Rs. 6534
    
    
16. Calculate the time in which the simple interest on Rs. 4000 at the rate of 5% per annum will be same as simple interest on Rs. 5000 at 8% per annum for 3 years.
    Solution:
    Let the required time = T years
    
    ⇒40×5×T=50×8×3
    ⇒ T = 6
    
    
    
17. Write the shaded and unshaded parts in the below figure in the form of fraction, percentage and decimal.
    
    Solution:
    
    
    
18. A tank A of capacity 70 litres is filled with water. For cleaning purpose, 30% of it is used and the remaining water was poured in another tank B of capacity 50 litres. How much percent of tank B is filled with water?
    
    Solution:
    Capacity of tank A = 70 litres
    Percentage of water used for cleaning = 30%
    Percentage of remaining water = (100 – 30) % = 70%
    That means, amount of water poured in tank B 
    Therefore, percentage of tank B filled with water 
    
    
19. Consider numbers 31 to 60. Find the percentage of numbers having digit 9 in the unit’s place.
    Solution:
    Total numbers = 30
    Numbers with unit’s place 9 are 39, 49 and 59.
    Therefore, percentage of numbers having digit 9 in unit’s place
    
    
20. Samidha distributed 37% of her bonus salary to Ashrams, 33% to Hospitals and the remaining Rs. 12000 she kept for her mother. Find the amount given to Ashrams and Hospitals.
    Solution:
    Let the bonus salary of Samidha = Rs. P
    Percentage of amount given to mother = 100 – (37 + 33) = 30%
    ⇒ 30% of P = 12000
    
    ⇒P=Rs.40000
    Amount given to Ashrams
    Amount given to Hospitals =