## NCERT Solutions for class 7 Maths Chapter 8: Comparing Quantities## Exercise 8.1
1₹ = 100 paise 5₹ = 5 × 100 = 500 paise Ratio = 500/50 Ratio = 10/1 Ratio = 10: 1
1 kg = 1000 g 15 kg = 15000 g Ratio = 15000/210 Ratio = (15 × 2 × 500)/ (15 × 2 × 7) Cancelling out the common terms, we get: Ratio = 500/7 Ratio = 500: 7
To find the ratio, both the units should be same. 1 m = 100 cm 9 m = 900 cm Ratio = 900 cm/ 27 cm Ratio = (9 × 100) (9 × 3) Ratio = 100/3 Ratio = 100: 3
1 day = 24 hours 30 days = 24 × 30 = 720 hours Ratio = 720 hours/36 hours 720 = 36 × 20 Ratio = (36 × 20)/ 36 Ratio = 20/1 = 20: 1
Number of computers for 1 student = 3/6 = 1/2 Number of computers for 24 students = 1/2 × 24 = 24/2 = 12 Thus, 12 computers will be needed for 24 students.
People per km People per km People per km (570 = 190 × 3) People per km People per km People per km (1660 = 830 × 2)
People per km People per km People per km Hence, Rajasthan is less populated. ## Exercise 8.2
1/8 × 100 = 100/8 = 12.5 % Thus, fraction 1/8 is equivalent to 12.5%.
5/4 × 100 = (5 × 100)/4 = 500/4 = 125 % Thus, fraction 5/4 is equivalent to 125%.
3/40 × 100 = (3 × 100)/40 = 300/40 = 7.5 % Thus, fraction 3/40 is equivalent to 7.5%.
2/7 × 100 = (2 × 100)/7 = 200/7 = 28.57% Or 200/7 = 196/7 + 4/7 (28 × 7 = 196) 200/7 = 28 4/7%
To convert a fraction to the percentage, we need to multiply the given fraction by 100. 65/100 × 100 = 65% Thus, the decimal fraction 0.65 is equivalent to 65%.
To convert a fraction to the percentage, we need to multiply the given fraction by 100. 21/10 × 100 = (21 × 100)/10 = 210 % Thus, the decimal fraction 2.1 is equivalent to 210%.
To convert a fraction to the percentage, we need to multiply the given fraction by 100. 2/100 × 100 = 2% Thus, the decimal fraction 0.02 is equivalent to 2%.
To convert a fraction to the percentage, we need to multiply the given fraction by 100. 1235/100 × 100 = (1235 × 100)/100 = 1235 % Thus, the decimal fraction 12.35 is equivalent to 1235%.
Fraction = Number of coloured parts/ Total number of parts Fraction = 1/4 To convert a fraction to the percentage, we need to multiply the given fraction by 100. 1/4 × 100 = 100/4 = 25 % Thus, fraction 1/4 is equivalent to 25%.
Fraction = Number of coloured parts/ Total number of parts Fraction = 3/5 To convert a fraction to the percentage, we need to multiply the given fraction by 100. 3/5 × 100 = (3 × 100)/5 = 300/5 = 60 % Thus, fraction 3/5 is equivalent to 60%.
Fraction = Number of coloured parts/ Total number of parts Fraction = 3/8 To convert a fraction to the percentage, we need to multiply the given fraction by 100. 3/8 × 100 = (3 × 100)/8 = 300/8 = 37.5 % Thus, fraction 3/8 is equivalent to 37.5%.
15 % = 15/100 15/100 × 250 = (15 × 250)/100 = 3750/100 = 37.5
1 % = 1/100 1/100 × 1 hour 1 hour = 60 minutes 1 minute = 60 seconds 1 hour = 60 × 60 = 3600 seconds 1/100 × 3600 = (1 × 3600)/100 = 3600/100 = 36 seconds
1 % = 1/100 1/100 × 1 hour 1 hour = 60 minutes = 1/100 × 60 = (1 × 60)/100 = 6/10 = 3/5 minutes
20% = 20/100 = 20/100 × 2500 = (20 × 2500)/100 = ₹ 500
75 % = 75/100 1 kg = 1000 g 75/100 × 1000 = (75 × 1000)/ 100 = 750 g Or 75/100 × 1 = (75 × 1)/ 100 = 0.75 kg
Let the whole quantity be A. 5 % of A = 600 5% = 5/100 5/100 × A = 600 A = (600 × 100)/5 A = 12000 Thus, the whole quantity is equivalent to 12000.
Let the whole quantity be A. 12 % of A = 1080 12% = 12/100 12/100 × A = 1080 A = (1080 × 100)/12 A = 9000 Thus, the whole quantity is equivalent to ₹9000.
Let the whole quantity be A. 40 % of A = 500 40% = 40/100 40/100 × A = 500 A = (500 × 100)/40 A = 1250 km Thus, the whole quantity is equivalent to 1250 km.
Let the whole quantity be A. 70 % of A = 14 70% = 70/100 70/100 × A = 14 A = (14 × 100)/70 A = 20 minutes Thus, the whole quantity is equivalent to 20 minutes.
Let the whole quantity be A. 40 % of A = 500 40% = 40/100 40/100 × A = 500 A = (500 × 100)/40 A = 1250 km Thus, the whole quantity is equivalent to 1250 km.
25% = 25/100 = 0.25 Let's factorise the numbers in the numerator and denominator. = (5 × 5)/ (2 × 2 × 5 × 5) = 1/4
150% = 150/100 = 1.5 Let's factorise the numbers in the numerator and denominator. = (5 × 5 × 2 × 3)/ (2 × 2 × 5 × 5) = 3/2
20% = 20/100 = 0.2 Let's factorise the numbers in the numerator and denominator. = (5 × 2 × 2)/ (2 × 2 × 5 × 5) = 1/5
5% = 5/100 = 0.05 Let's factorise the numbers in the numerator and denominator. = (5)/ (2 × 2 × 5 × 5) = 1/20
Percentage of males = 40 Remaining percentage = 100 - percentage of females - percentage of males = 100 - 30 - 40 = 30 Thus, the remaining percentage of children is 30%.
Percentage of voters who did not vote = 100 - percentage of voters who vote = 100 - 60 = 40% Number of voters who did not vote = 40% of 15000 = 40/100 × 15000 = (40 × 15000)/ 100 = 6000
10% of A = ₹4000 10/100 × A = 4000 A = (4000 × 100)/10 A = 40,000 Thus, the total salary of Meeta is ₹40,000.
= 25 % of 20 = 25/100 × 20 = (25 × 20)/100 = 500/100 = 5 Thus, the cricket team won 5 numbers of matches. ## Exercise 8.3
Selling price of the gardening shears (SP) = ₹ 325 If SP > CP, there is a profit. Profit = SP - CP Profit = ₹ 325 - ₹ 250 Profit = ₹ 75 Profit % = Profit/CP × 100 Profit % = 75/250 × 100 Profit % = 30 Thus, the profit is ₹ 75 and the profit percentage is 30%.
Selling price of the refrigerator (SP) = ₹ 13,500 If SP > CP, there is a profit. Profit = SP - CP Profit = ₹ 13500 - ₹ 12000 Profit = ₹ 1500 Profit % = Profit/CP × 100 Profit % = 1500/12000 × 100 Profit % = 12.5 Thus, the profit is ₹ 1500 and the profit percentage is 12.5%.
Selling price of the cupboard (SP) = ₹ 3000 If SP > CP, there is a profit. Profit = SP - CP Profit = ₹ 3000 - ₹ 2500 Profit = ₹ 500 Profit % = Profit/CP × 100 Profit % = 500/2500 × 100 Profit % = 20 Thus, the profit is ₹ 500 and the profit percentage is 20%.
Selling price of the skirt (SP) = ₹ 150 If SP < CP, there is a loss. Loss = CP - SP Loss = 250 - 100 Loss = ₹ 100 Loss % = Loss/CP × 100 Loss % = 100/250 × 100 Loss % = 40 Thus, the loss is ₹ 100 and the loss percentage is 40 %.
Ratio percentage = 3/ (3 + 1) × 100 Ratio percentage = 3/4 × 100 Ratio percentage = 75 % Ratio percentage of the second number = Given ratio/ Total × 100 Ratio percentage = 1/ (3 + 1) × 100 Ratio percentage = 1/4 × 100 Ratio percentage = 25 %
Ratio percentage = 2/ (2 + 3 + 5) × 100 Ratio percentage = 2/10 × 100 Ratio percentage = 20 % Ratio percentage of the second number = Given ratio/ Total × 100 Ratio percentage = 3/ (2 + 3 + 5) × 100 Ratio percentage = 3/10 × 100 Ratio percentage = 30 % Ratio percentage of the third number = Given ratio/ Total × 100 Ratio percentage = 5/ (2 + 3 + 5) × 100 Ratio percentage = 5/10 × 100 Ratio percentage = 50 %
Ratio percentage = 1/ (1 + 4) × 100 Ratio percentage = 1/5 × 100 Ratio percentage = 20 % Ratio percentage of the second number = Given ratio/ Total × 100 Ratio percentage = 4/ (1 + 4) × 100 Ratio percentage = 4/5 × 100 Ratio percentage = 80 %
Ratio percentage = 1/ (1 + 2 + 5) × 100 Ratio percentage = 1/8 × 100 Ratio percentage = 12.5 % Ratio percentage of the second number = Given ratio/ Total × 100 Ratio percentage = 2/ (1 + 2 + 5) × 100 Ratio percentage = 2/8 × 100 Ratio percentage = 25 % Ratio percentage of the third number = Given ratio/ Total × 100 Ratio percentage = 5/ (1 + 2 + 5) × 100 Ratio percentage = 5/8 × 100 Ratio percentage = 62.5 %
= 500 Percentage decrease = Difference in the population/Original population × 100 Percentage decrease = 500/25000 × 100 Percentage decrease = 2%
Selling price of the car (SP) = ₹3,70,000 SP > CP Hence, there is a profit. Increased amount = ₹3,70,000 - ₹ 3,50,000 Increased amount = ₹ 20,000 Percentage increase = Increase amount/CP × 100 Percentage increase = 20,000/3,50,000 × 100 Percentage increase = 5.55% Or Percentage increase = 40/7 % = 35/7 % + 5/7 % = 5% + 5/7% = 5 5/7%
Profit % = 20 20 % of 10,000 = 20/100 × 10000 Profit = ₹ 2000 Selling Price of TV = CP + Profit Selling Price of TV = ₹ 10,000 + ₹ 2000 Selling Price of TV = ₹ 12,000
Loss % = 20 Cost price of the washing machine = [(100)/ (100 - Loss %) × SP = 100/80 × 13,500 = (100 × 13,500)/ 80 = ₹ 16875 Thus, the washing machine was bought at the price of ₹ 16875.
Percentage of carbon = 3/ (10 + 3 + 12) × 100 Percentage of carbon = 3 / 25 × 100 Percentage of carbon = (3 × 100)/25 = 12 % Thus, the percentage of carbon in the chalk is 12 %.
Percentage of carbon in the chalk = 12 % 12 % of A = 3 g 12/100 × A = 3 A = (3 × 100)/ 12 A = 25 g Thus, the weight of the chalk stick is 25 g.
Loss % = 15 % Loss = Loss % × CP Loss = 15 % × 275 Loss = 15/100 × 275 Loss = (15 × 275)/100 Loss = ₹ 41.25 Selling price of the book = Cost price - Loss Selling price of the book = ₹ 275 - ₹ 41.25 Selling price of the book = ₹ 233.75 Thus, Amina sold the book for ₹ 233.75.
Interest = (P × R × T)/100 Principal = ₹ 1,200 Rate = 12 % Time = 3 years Interest = (1200 × 12 × 3)/ 100 Interest = ₹ 432 Amount = principal + Interest Amount = ₹ 1,200 + ₹ 432 Amount = ₹ 1,632
Interest = (P × R × T)/100 Principal = ₹ 7,500 Rate = 5 % Time = 3 years Interest = (7500 × 5 × 3)/ 100 Interest = ₹ 1125 Amount = principal + Interest Amount = ₹ 7,500 + ₹ 1125 Amount = ₹ 8,625
Principal = ₹ 56,000 Rate =? Time = 2 years Interest = ₹ 280 R = (Interest × 100)/ (P × T) R = (280 × 100)/ (56,000 × 2) R = 1/4 % R = 0.25 % Thus, 0.25 % is the rate that gives ₹ 280 as interest on a sum of ₹ 56,000 in 2 years.
Principal =? Rate = 9% Time = 1 year Interest = ₹ 45 P = (Interest × 100)/ (R × T) P = (45 × 100)/ (9 × 1) P =₹ 500 Thus, Meena has borrowed rupees 500 that gives an interest of ₹45 for one year at 9% rate p.a. |