{"id":10998,"date":"2021-04-20T14:47:06","date_gmt":"2021-04-20T09:17:06","guid":{"rendered":"https:\/\/apboardsolutions.guru\/?p=10998"},"modified":"2021-09-15T11:33:33","modified_gmt":"2021-09-15T06:03:33","slug":"ap-board-6th-class-maths-solutions-chapter-6-ex-6-1","status":"publish","type":"post","link":"https:\/\/apboardsolutions.guru\/ap-board-6th-class-maths-solutions-chapter-6-ex-6-1\/","title":{"rendered":"AP Board 6th Class Maths Solutions Chapter 6 Basic Arithmetic Ex 6.1"},"content":{"rendered":"

AP State Syllabus AP Board 6th Class Maths Solutions<\/a> Chapter 6 Basic Arithmetic Ex 6.1 Textbook Questions and Answers.<\/p>\n

AP State Syllabus 6th Class Maths Solutions 6th Lesson Basic Arithmetic Ex 6.1<\/h2>\n

Question 1.
\nExpress the following in the terms of ratios.
\ni) The length of a rectangle is 5 times to its breadth.
\nii) For preparing coffee, 2 cups of water require to 1 cup of milk.
\nAnswer:
\ni) Let the breadth of rectangle = x = 1 part
\nlength of rectangle = 5x = 5 parts
\nRatio = length : breadth = 5x : x = \\(\\frac{5x}{x}\\) = \\(\\frac{5}{1}\\) = 5 : 1<\/p>\n

ii) To prepare coffee,
\nRequired cups of water = 2
\nRequired cups of milk = 1
\nRatio = water : milk = 2 : 1<\/p>\n

\"AP<\/p>\n

Question 2.
\nExpress the following in the simplest form.
\ni) 24 : 9
\nii) 144 : 12
\niii) 961 : 31
\niv) 1575 : 1190
\nAnswer:
\ni) 24 : 9
\nGiven ratio is 24 : 9
\nTo write the given ratio in the simplest form.
\nFirst find the HCF of two terms.
\n\"AP
\nHCF of 24 and 9 is 3.
\nThen, divide each term by their HCF.
\nSimplest form of the ratio = 24 \u00f7 3 : 9 \u00f7 3
\nRequired ratio = 8 : 3<\/p>\n

ii) 144 : 12
\nGiven ratio is 144 : 12
\nTo write the given ratio in the simplest form.
\nFirst find the HCF of two terms.
\n\"AP
\nHCF of 144 and 12 is 12.
\nThen, divide each term by their HCF.
\nSimplest form of the ratio = 144 \u00f7 12 : 12 \u00f7 12
\nRequired ratio = 12 : 1<\/p>\n

\"AP<\/p>\n

iii) 961 : 31
\nGiven ratio is 961 : 31
\nTo write the given ratio in the simplest form.
\nFirst find the HCF of two terms.
\n\"AP
\nHCF of 961 and 31 is 31.
\nThen, divide each term by their HCF.
\nSimplest form of the ratio = 961 \u00f7 31 : 31 \u00f7 31
\nRequired ratio = 31 : 1<\/p>\n

iv) 1575 : 1190
\nGiven ratio is 1575 : 1190
\nTo write the given ratio in the simplest form.
\nFirst find the HCF of two terms.
\n\"AP
\nHCF of 1575 and 1190 is 35.
\nThen, divide each term by their HCF.
\nSimplest form of the ratio = 1575 \u00f7 35 : 1190 \u00f7 35
\n\u2234 Required ratio = 45 : 34<\/p>\n

Question 3.
\nWrite the antecedents and consequents of the following ratios.
\n(i) 36 : 73
\n(ii) 65 : 84
\n(iii) 58 : 97
\n(iv) 69 : 137
\nAnswer:<\/p>\n\n\n\n\n\n\n\n
S.No.<\/td>\nRatio<\/td>\nAntecedents<\/td>\nConsequents<\/td>\n<\/tr>\n
(i)<\/td>\n36: 73<\/td>\n36<\/td>\n73<\/sup><\/td>\n<\/tr>\n
(ii)<\/td>\n65 : 84<\/td>\n65<\/td>\n84<\/td>\n<\/tr>\n
(iii)<\/td>\n58:97<\/td>\n58<\/td>\n97<\/td>\n<\/tr>\n
(iv)<\/td>\n69 : 137<\/td>\n69<\/td>\n137<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"AP<\/p>\n

Question 4.
\nFind the ratios of the following in their simplest form.
\ni) 25 minutes to 55 minutes
\nii) 45 seconds to 30 minutes
\niii) 4 m 20 cm to 8 m 40 cm
\niv) 5 litres to 0.75 litres
\nv) 4 weeks to 4 days
\nvi) 5 dozen to 2 scores (1 score = 20 items)
\nAnswer:
\ni) 25 minutes to 55 minutes
\nGiven 25 minutes to 55 minutes = 25 : 55
\n\"AP
\nHCF of 25 and 55 is 5 = 25 \u00f7 5 : 55 \u00f7 5 (Divide each term by 5)
\n\u2234 Required ratio = 5:11<\/p>\n

ii) 45 seconds to 30 minutes
\nGiven 45 seconds to 30 minutes.
\nTo write the given ratio in the simplest form.
\nFirst convert the two terms into same units.
\n1 minute = 60 seconds
\n30 minutes = 30 \u00d7 60 = 1800 seconds
\nThen, find the HCF of two terms and divide them by their HCF.
\n\"AP
\nHCF of 45 and 1800 is 45.
\n= 45 \u00f7 45 : 1800 \u00f7 45 (divide each term by 45)
\n\u2234 Required ratio = 1 : 40<\/p>\n

\"AP<\/p>\n

iii) 4 m 20 cm to 8 m 40 cm
\nGiven 4 m 20 cm to 8 m 40 cm
\nTo write the given ratio in the simplest form.
\nFirst we convert them into cm.
\n1 m = 100 cm
\n4 m = 400 cm
\n8 m = 800 cm
\n4 m 20 cm = 400 + 20 = 420 cm
\n8 m 40 cm = 800 + 40 = 840 cm
\nThen, find the HCF of 420 and 840 and divide them by HCF.
\n\"AP
\nHCF of 420 and 840 is 420.
\n= 420 \u00f7 420 : 840 \u00f7 420 (divide each term by 420)
\nRequired ratio = 1 : 2.<\/p>\n

iv) 5 litres to 0.75 litres
\nGiven 5 litres to 0.75 litres
\nTo write the given ratio in the simplest form, first we convert litres into millilitres.
\n1 litre = 1000 ml
\n5 litres = 5000 ml
\n0.75 litres = 750 ml
\nThen, find the HCF of 5000; 750 and divide them by HCF.
\n\"AP
\nHCF of 5000 and 750 is 250,
\n= 5000 \u00f7 250 : 750 \u00f7 250 (divide each term by 250)
\nRequired ratio = 20 : 3<\/p>\n

\"AP<\/p>\n

v) 4 weeks to 4 days
\nGiven 4 weeks to 4 days.
\nTo write the given ratio in the simplest form, first we convert them into same units (days).
\n1 week = 7 days
\n4 weeks = 4 \u00d7 7 = 28 days
\nThen, find the HCF of 28 and 4, then divide them by HCF.
\n\"AP
\nHCF of 28 and 4 is 4 = 28 \u00f7 4 : 4 \u00f7 4 (divide each term by 4)
\nRequired ratio = 7 : 1<\/p>\n

vi) 5 dozen to 2 scores (1 score = 20 items)
\nGiven 5 dozen to 2 scores.
\nTo write the given ratio in the simplest form, first we convert them into same units.
\n1 dozen = 12 items
\n5 dozens = 5 \u00d7 12 = 60 items
\n1 score = 20 items
\n2 scores = 2 \u00d7 20 = 40 items
\nThen, find the HCF of 60 and 40, divide them by HCF.
\n\"AP
\nHCF of 60 and 40 is 20 = 60 \u00f7 20 : 40 \u00f7 20 (divide each term by 20)
\nRequired ratio = 3 : 2<\/p>\n

\"AP<\/p>\n

Question 5.
\nRahim works in a software company and earns Rs. 75,000\/- per month. He saves Rs. 28,000\/- per month from his earnings. Find the ratio of
\ni) His savings to his income
\nii) His income to his expenditure
\niii) His savings to his expenditure
\nAnswer:
\nGiven Rahim’s monthly income = Rs. 75000
\nmonthly savings = Rs. 28000
\nMonthly expenditure = income – savings
\n= 75000 – 28000 = 47,000\/-
\ni) Ratio of savings to income = 28000 : 75000
\nTo convert the ratio into the simplest form divide each term by their HCF is 1000
\n= 28000 \u00f7 1000 : 75000 \u00f7 1000 (divide by 1000)
\n= 28 : 75
\nRequired ratio of savings to income = 28 : 75<\/p>\n

ii) Ratio of income to expenditure = 75000 : 47000
\nTo convert the ratio into the simplest form divide each term by their HCF is 1000 = 75000 \u00f7 1000 : 47000 \u00f7 1000 (divide by 1000)
\n= 75 : 47
\nRequired ratio of income to expenditure = 75 : 47<\/p>\n

iii) Ratio of savings to expenditure = 28000 : 47000
\nTo convert the ratio into the simplest form divide each term by their HCF is 1000 = 28000 \u00f7 1000 : 47000 \u00f7 1000 (divide by 1000)
\n= 28 : 47
\nRequired ratio of savings to expenditure = 28 : 47<\/p>\n","protected":false},"excerpt":{"rendered":"

AP State Syllabus AP Board 6th Class Maths Solutions Chapter 6 Basic Arithmetic Ex 6.1 Textbook Questions and Answers. AP State Syllabus 6th Class Maths Solutions 6th Lesson Basic Arithmetic Ex 6.1 Question 1. Express the following in the terms of ratios. i) The length of a rectangle is 5 times to its breadth. ii) …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[10],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/10998"}],"collection":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/comments?post=10998"}],"version-history":[{"count":0,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/10998\/revisions"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/media?parent=10998"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/categories?post=10998"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/tags?post=10998"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}