{"id":25205,"date":"2021-06-22T12:45:37","date_gmt":"2021-06-22T07:15:37","guid":{"rendered":"https:\/\/ncertsolutions.guru\/?p=25205"},"modified":"2021-06-30T18:04:47","modified_gmt":"2021-06-30T12:34:47","slug":"ncert-solutions-for-class-6-maths-chapter-12-ex-12-1","status":"publish","type":"post","link":"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-6-maths-chapter-12-ex-12-1\/","title":{"rendered":"NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion Ex 12.1"},"content":{"rendered":"

These NCERT Solutions for Class 6 Maths<\/a> Chapter 12 Ratio and Proportion Ex 12.1 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\n

NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion Exercise 12.1<\/h2>\n

Question 1.
\nThere are 20 girls and 15 boys in a class.
\n(a) What is the ratio of number of girls to the number of boys?
\n(b) What is the ratio of number of girls to the total number of students in the class?
\nAnswer:
\n(a) The ratio of girls to that of boys = \\(\\frac{20}{15}=\\frac{4}{3}\\) = 4 : 3<\/p>\n

(b) The ratio of girls to total students = \\(\\frac{20}{20+15}=\\frac{20}{35}=\\frac{4}{7}\\) = 4 : 7<\/p>\n

\"NCERT<\/p>\n

Question 2.
\nOut of 30 students in a class, 6 like football, 12 like cricket and remaining like tennis. Find the ratio of
\n(a) Number of students liking football to number of students liking tennis.
\n(b) Number of students liking cricket to total number of students.
\nAnswer:
\nTotal number of students = 30
\nNumber of students like football = 6
\nNumber of students like cricket = 12
\nThus number of students like tennis = 30 – 6 – 12 = 12<\/p>\n

(a) The ratio of students like football that of tennis = \\(\\frac{6}{12}=\\frac{1}{2}\\) = 1 : 2
\n(b) The ratio of students like cricket to that of total students = \\(\\frac{12}{30}=\\frac{2}{5}\\) = 2.5<\/p>\n

Question 3.
\nSee the figure and find the ratio of
\n(a) Number of triangles to the number of circles inside the rectangle.
\n(b) Number of squares to all the figures inside the rectangle.
\n(c) Number of circles to all the figures inside the rectangle.
\nAnswer:
\n(a) Ratio of number of triangle to that of circles = \\(\\frac{3}{2}\\) = 3 : 2
\n(b) Ratio of number of squares to all figures = \\(\\frac{2}{7}\\) = 2 : 7
\n(c) Ratio of number of circles to all figures = \\(\\frac{2}{7}\\) = 2 : 7<\/p>\n

\"NCERT<\/p>\n

Question 4.
\nDistances travelled by Hamid and Akhtar in an hour are 9 km and 12 km. Find the ratio of speed of Hamid to the speed of Akhtar.
\nAnswer:
\nWe know that, Speed = \\(\\frac{\\text { Distance }}{\\text { Time }}\\)
\nSpeed of Hamid = \\(\\frac{9 \\mathrm{~m}}{1 \\mathrm{~h}}\\) = 9 km\/h and Speed of Akhtar \\(\\frac{12 \\mathrm{~m}}{1 \\mathrm{~h}}\\) = 12 km\/h
\nRatio of speed of Hamid to that of speed of Akhtar = \\(\\frac{9}{12}=\\frac{3}{4}\\) = 3 : 4<\/p>\n

Question 5.
\nFill in the following blanks:
\nAnswer:
\n\"NCERT
\nYes, these are equivalent ratios.<\/p>\n

Question 6.
\nFind the ratio of the following:
\n(a) 81 to 108
\n(b) 98 to 63
\n(c) 33 km to 121 km
\n(d) 30 minutes to 45 minutes
\nAnswer:
\n(a) Ratio of 81 to 108
\n= \\(\\frac{81}{108}=\\frac{3}{4}\\) = 3 : 4<\/p>\n

(b) Ratio of 98 to 63
\n= \\(\\frac{98}{63}=\\frac{14}{9}\\) = 14 : 9<\/p>\n

(c) Ratio of 33 km to 121 km
\n= \\(\\frac{33}{121}=\\frac{3}{11}\\) = 3 : 11<\/p>\n

(d) Ratio of 30 minutes to 45 minutes
\n= \\(\\frac{30}{45}=\\frac{2}{3}\\) = 2 : 3<\/p>\n

\"NCERT<\/p>\n

Question 7.
\nFind the ratio of the following:
\n(a) 30 minutes to 1.5 hours
\n(b) 40 cm to 1.5 m
\n(c) 55 paise to \u20b9 1
\n(d) 500 mL to 2 litres
\nAnswer:
\n(a) 30 minutes to 1.5 hour
\n1.5 hours = 1.5 \u00d7 60 = 90 minutes
\n[\u2235 1 hour = 60 minutes]
\nNow, ratio of 30 minutes to 1.5 hour = 30 minutes: 1.5 hour
\n\u21d2 30 minutes : 90 minutes
\n= \\(\\frac{30}{90}=\\frac{1}{3}\\) = 1 : 3<\/p>\n

(b) 40 cm to 1.5 m
\n1.5 m = 1.5 \u00d7 100 cm = 150 cm
\n[\u2235 1 m = 100 cm]
\nNow. ratio of 40 cm to 1.5 m
\n= 40 cm : 1.5 m
\n\u21d2 40 cm : 150 cm
\n= \\(\\frac{40}{150}=\\frac{4}{15}\\) = 4 : 15<\/p>\n

(c) 55 paise to \u20b9 1
\nRs 1 = 100 paise
\nNow, ratio of 55 paise to \u20b9 1
\n= 55 paise : 100 paise
\n\u21d2 \\(\\frac{55}{100}=\\frac{11}{20}\\) = 11 : 20<\/p>\n

(d) 500 ml to 2 litters
\n2 litres = 2 \u00d7 1000 ml = 2000 ml
\n[\u2235 litre = 1000 ml]
\nNow, ratio of 500 ml to 2 litres
\n= 500 m 1 : 2 litres
\n\u21d2 500 ml : 2000 ml
\n= \\(\\frac{500}{2000}=\\frac{1}{4}\\) = 1 : 4<\/p>\n

Question 8.
\nIn a year, Seema earns \u20b9 1, 50, 000 and saves \u20b9 50,000. Find the ratio of
\n(a) Money that Seema earns to the money she saves.
\n(b) Money that she saves to the money she spends.
\nAnswer:
\nTotal earning
\n= \u20b9 1,50,000 and Saving = \u20b9 50,000
\n\u2235 Money spent
\n= \u20b9 1,50,000 – \u20b9 50,000 = \u20b9 1,00,000<\/p>\n

(a) Ratio of money earned to money
\nsaved = \\(\\frac{150000}{50000}=\\frac{3}{1}\\) = 3 : 1<\/p>\n

(b) Ratio of money saved to money
\nspend = \\(\\frac{50000}{100000}=\\frac{1}{2}\\) = 1 : 2<\/p>\n

\"NCERT<\/p>\n

Question 9.
\nThere are 102 teachers in a school of 3300 students. Find the ratio of the number of teachers to the number of students.
\nAnswer:
\nRatio of number of teachers to that of studends = \\(\\frac{102}{3300}=\\frac{17}{550}\\) = 17 : 550<\/p>\n

Question 10.
\nIn a college, out of 4320 students, 2300 are girls. Find the ratio of
\n(a) Number of girls to the total number of students.
\n(b) Number of boys to the number of girls.
\n(c) Number of boys to the total number of students.
\nAnswer:
\nTotal number of students in school = 4320
\nNumber of girls = 2300
\nTherefore, number of boys = 4320 – 2300 – 2020<\/p>\n

(a) Ratio of girls to total number of students = \\(\\frac{2300}{4320}=\\frac{115}{216}\\) = 115 : 216<\/p>\n

(b) Ratio of boys to that of girls = \\(\\frac{2020}{2300}=\\frac{101}{115}\\) = 101 : 115<\/p>\n

(c) Ratio of boys to total number of students = \\(\\frac{2020}{4320}=\\frac{101}{216}\\) = 101 : 216<\/p>\n

Question 11.
\nOut of 1800 students in a school, 750 opted basketball, 800 opted cricket and remaining opted table tennis. If a student can opt only one game, find the ratio of
\n(a) Number of students who opted basketball to the number of students who opted table tennis.
\n(b) Number of students who opted cricket to the number of students opting basketball.
\n(c) Number of students who opted basketball to the total number of students.
\nAnswer:
\nTotal number of students = 1800
\nNumber of students opted basketball = 750
\nNumber of students opted cricket = 800
\nTherefore, number of students opted tennis = 1800 – (750 + 800) – 250<\/p>\n

(a) Ratio of students opted basketball to that of opted table tennis
\n= \\(\\frac{750}{250}=\\frac{3}{1}\\) = 3 : 1<\/p>\n

(b) Ratio of students opted cricket to students opted basketball
\n= \\(\\frac{750}{1800}=\\frac{5}{12}\\) = 16 : 15<\/p>\n

(c) Ratio of students opted basketball to total no. of students
\n= \\(\\frac{750}{1800}=\\frac{5}{12}\\) = 5 : 12<\/p>\n

\"NCERT<\/p>\n

Question 12.
\nCost of a dozen pens is \u20b9 180 and cost of 8 ball pens is \u20b9 56. Find the ratio of the cost of a pen to the cost of a ball pen.
\nAnswer:
\nCost of a dozen pens (12 pens) = \u20b9 180
\n\u2234 Cost of 1 pen = \\(\\frac{180}{2}\\) = \u20b9 15
\nCost of 8 ball pens = \u20b9 56
\n\u2234 Cost of 1 ball pen = \\(\\frac{56}{8}\\) = \u20b9 7
\nRatio of cost of one pen to that of one ball pen = \\(\\frac{15}{7}\\) = 15 : 7<\/p>\n

Question 13.
\nConsider the statement: Ratio of breadth and length of a hall is 2 : 5. Complete the following table that shows some possible breadths and lengths of the hall.
\n\"NCERT
\nAnswer:
\nRatio of breadth to length = 2 : 5 = \\(\\frac{2}{5}\\)
\n\u2234 Other equivalent ratios are
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 14.
\nDivide 20 pens between Sheela and Sangeeta in the ratio of 3 : 2.
\nAnswer:
\nRatio between Sheela and Sangeeta = 3 : 2
\nTotal these terms = 3 + 2 = 5
\nTherefore, the part of Sheela = \\(\\frac{2}{5}\\) of the total pens and the part of Sangeeta = \\(\\frac{2}{5}\\) of total pens
\nThus, Sheela gets = \\(\\frac{3}{5}\\) x 20 = 12 pens and Sangeeta gets = \\(\\frac{2}{5}\\) x 20 = 8 pens<\/p>\n

Question 15.
\nMother wants to divide \u20b9 36 between her daughters Shreya and Bhoomika in the ratio of their ages. If age of Shreya is 15 years and age of Bhoomika is 12 years, find how much Shreya and Bhoomika will get.
\nAnswer:
\nRatio of the age of Shreya to that of Bhoomika = \\(\\frac{15}{12}=\\frac{5}{4}\\) = 5 : 4
\nThus, \u20b9 36 divide between Shreya and Bhoomika in the ratio of 5 : 4.
\nShreya gets = \\(\\frac{5}{9}\\) of \u20b9 36 = \\(\\frac{5}{9}\\) \u00d7 36 = \u20b9 20 Bhoomika gets = \\(\\frac{4}{9}\\) of \u20b9 36 = \\(\\frac{4}{9}\\) \u00d7 36 = \u20b9 16<\/p>\n

\"NCERT<\/p>\n

Question 16.
\nPresent age of father is 42 years and that of his son is 14 years. Find the ratio of
\n(a) Present age of father to the present age of son.
\n(b) Age of the father to the age of son, when son was 12 years old.
\n(c) Age of father after 10 years to the age of son after 10 years.
\n(d) Age of father to the age of son when father was 30 years old.
\nAnswer:
\n(a) Ratio of father\u2019s present age to that of son = \\(\\frac{42}{14}=\\frac{3}{1}\\) = 3 : 1<\/p>\n

(b) When son was 12 years, i.e., 2 years ago, then father was (42 – 2) = 40
\nTherefore, the ratio of their ages = \\(\\frac{40}{12}=\\frac{10}{3}\\) = 10 : 3<\/p>\n

(c) Age of father after 10 years
\n= 42 + 10 = 52 years
\nAge of son after 10 years
\n= 14 + 10 = 24 years
\nTherefore, ratio of their ages = \\(\\frac{52}{24}=\\frac{13}{6}\\) = 13 : 6<\/p>\n

(d) When father was 30 years old, i.e., 12 years ago, then son was (14 – 12] = 2 years old
\nTherefore, the ratio of their ages
\n= \\(\\frac{30}{2}=\\frac{15}{1}\\) = 15 : 1<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion Ex 12.1 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion Exercise 12.1 Question 1. There are 20 girls and 15 boys in a class. (a) What is the ratio …<\/p>\n

NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion Ex 12.1<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[10],"tags":[],"yoast_head":"\nNCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion Ex 12.1 - NCERT Solutions<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-6-maths-chapter-12-ex-12-1\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion Ex 12.1 - NCERT Solutions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion Ex 12.1 Questions and Answers are prepared by our highly skilled subject experts. 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NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion Exercise 12.1 Question 1. There are 20 girls and 15 boys in a class. 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