Comparing Quantities Worksheet Maths CBSE Class 7 Sample Paper

Comparing Quantities Worksheet

Multiple Choice Questions

Consider two numbers P and Q. When these two numbers are added, the sum is equal to $begin mathsize 11px style 21 over 15 end style$ of number P. What percent is number Q of number P?
(a) $begin mathsize 11px style 21 over 15 percent sign end style$
(b) $begin mathsize 11px style 15 over 21 percent sign end style$
(c) 60%
(d) 30%
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
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%
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%
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
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
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.
Find the value of 10% of greatest 2-digit even number.
The cost price and selling price of two flowers bouquets are given below.

Which bouquet will yield more profit? By how much percent?
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.
Identify the boxes equal to ‘2 hundredth’.
Find the percentage of shaded boxes from the below figure.
Swati makes rice by adding 3 cups of water to 2 cups of rice. Represent each of the ingredients used in rice as percentage.
For buying a flat on rent, Pooja had to put down a deposit of $begin mathsize 11px style 1 over 20 end style$ of the value of the flat. What percentage was this?
In 2022, the price of bicycle was Rs. 5400. If the price has been increased by 21% this year, find its price this year.
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.
Write the shaded and unshaded parts in the below figure in the form of fraction, percentage and decimal.
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?
Consider numbers 31 to 60. Find the percentage of numbers having digit 9 in the unit’s place.
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

Consider two numbers P and Q. When these two numbers are added, the sum is equal to $begin mathsize 11px style 21 over 15 end style$ of number P. What percent is number Q of number P?
(a) $begin mathsize 11px style 21 over 15 percent sign end style$
(b) $begin mathsize 11px style 15 over 21 percent sign end style$
(c) 60%
(d) 30%
Correct Option: (c) 60%
Solution:
$begin mathsize 11px style straight P plus straight Q equals 21 over 15 straight P rightwards double arrow straight Q equals 21 over 15 straight P minus straight P equals 3 over 5 straight P Let space straight Q space equals space straight x percent sign space of space straight P rightwards double arrow 3 over 5 straight P equals straight x over 100 straight P rightwards double arrow straight x space equals space 60 percent sign end style$
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,
$begin mathsize 11px style 25 over 100 cross times straight x equals 120 end style$
⇒x=480
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
$begin mathsize 11px style Interest space equals space fraction numerator straight P cross times straight T cross times straight R over denominator 100 end fraction space rightwards double arrow space 8250 space equals space fraction numerator 15000 cross times 5 cross times straight R over denominator 100 end fraction rightwards double arrow space straight R space equals space 11 percent sign end style$
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
$begin mathsize 11px style therefore end style$ Discount = Rs. (440 – 330) = Rs. 110
And, discount $begin mathsize 11px style percent sign equals 110 over 440 cross times 100 equals 25 percent sign end style$
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:
$begin mathsize 11px style fraction numerator begin display style 6 over 100 end style cross times 200 over denominator begin display style 11 over 100 end style cross times 100 end fraction equals fraction numerator straight k plus 1 over denominator straight k end fraction rightwards double arrow 12 over 11 equals fraction numerator straight k plus 1 over denominator straight k end fraction end style$
⇒ 12k = 11k + 11
⇒ k = 11
⇒ Sum of digits = 1 + 1 = 2
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 $begin mathsize 11px style equals 30 over 50 cross times 100 equals 60 percent sign end style$
Subjective Questions
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%
$begin mathsize 11px style therefore Savings space equals space 20 percent sign space of space Rs. space 25000 space equals 20 over 100 cross times 25000 space equals space Rs. space 5000 end style$
Find the value of 10% of greatest 2-digit even number.
Solution:
Greatest 2-digit even number = 98
Required value $begin mathsize 11px style equals 10 over 100 cross times 98 equals 9.8 end style$
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 $begin mathsize 11px style percent sign equals 50 over 300 cross times 100 equals 16.67 percent sign end style$
For Bouquet II,
Profit = SP – CP = Rs. (780 – 700) = Rs. 80
Profit $begin mathsize 11px style percent sign equals 80 over 700 cross times 100 equals 11.43 percent sign end style$
⇒ Profit% for bouquet I > Profit% for bouquet II
Therefore, bouquet I yields more profit than bouquet II.
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 $begin mathsize 11px style equals 20 over 100 cross times 40 equals 8 end style$
Number of kurtis which are ironed $begin mathsize 11px style equals 10 over 100 cross times 60 equals 6 end style$
So, number of clothes which are not ironed = 100 – 8 – 6 = 86
And, percentage of clothes which are not ironed $begin mathsize 11px style equals 86 over 100 cross times 100 equals 86 percent sign end style$
Identify the boxes equal to ‘2 hundredth’.

Solution:

2 hundredth $begin mathsize 11px style equals 0.02 equals 2 over 100 equals 2 percent sign end style$
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 $begin mathsize 11px style equals 3 over 10 cross times 100 equals 30 percent sign end style$
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 $begin mathsize 11px style equals 3 over 5 cross times 100 equals 60 percent sign end style$
Percentage of rice $begin mathsize 11px style equals 2 over 5 cross times 100 equals 40 percent sign end style$
For buying a flat on rent, Pooja had to put down a deposit of $begin mathsize 11px style 1 over 20 end style$ of the value of the flat. What percentage was this?
Solution:
$begin mathsize 11px style 1 over 20 equals fraction numerator 1 cross times 5 over denominator 20 cross times 5 end fraction equals 5 over 100 equals 5 percent sign end style$
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
$begin mathsize 11px style equals space Rs. space 5400 space plus 21 over 100 space cross times Rs.5400 end style$
= Rs. 5400 + Rs. 1134
= Rs. 6534
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
$begin mathsize 11px style fraction numerator 4000 cross times 5 cross times straight T over denominator 100 end fraction equals fraction numerator 5000 cross times 8 cross times 3 over denominator 100 end fraction end style$
⇒40×5×T=50×8×3
⇒ T = 6
Write the shaded and unshaded parts in the below figure in the form of fraction, percentage and decimal.

Solution:
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 $begin mathsize 11px style equals 70 over 100 cross times 70 equals 49 space litres end style$
Therefore, percentage of tank B filled with water $begin mathsize 11px style equals space 49 over 50 cross times 100 equals 98 percent sign end style$
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 $begin mathsize 11px style equals 3 over 30 cross times 100 equals 10 percent sign end style$
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
$begin mathsize 11px style rightwards double arrow 30 over 100 cross times straight P equals 12000 end style$
⇒P=Rs.40000
Amount given to Ashrams $begin mathsize 11px style equals 37 over 100 cross times 40000 equals Rs. space 14 comma 800 end style$
Amount given to Hospitals = $begin mathsize 11px style equals 33 over 100 cross times 40000 equals Rs. space 13 comma 200 end style$