Direction: Read the following information carefully and answer the given questions:<\/p>\n\n\n\n
There are four bags A, B, C and D in which balls of different colours-red, blue, yellow and white are present. The weight of a red ball, a blue ball, yellow ball and a white ball are 16 g, 20 g, 18 g and 24 g respectively. Total number of balls of all colourstogether is same in all the bags. Some information about the bags is given below:-<\/p>\n\n\n\n
Bag A: Ratio of number ofred and blue balls is 5:4. Number of yellow balls is 9 more than red balls. Ratio of weight of blue and white balls is<\/p>\n\n\n\n
10:13. Weight of all the yellow ballsin the bag is 432g.<\/p>\n\n\n\n
Bag B: Percentage of blue balls in B is 50% more than blue balls in A. Ratio of weight of blue balls and yellow balls is 1:1. Total weight of yellow and red balls togetheris 552 gm.<\/p>\n\n\n\n
Bag C: Number of red and blue balls together is<\/p>\n\n\n\n
29 and number of blue and white balls togetheris 28. Probability of choosing a ball which is not white is 25\/32.<\/p>\n\n\n\n
Bag D: Number ofYellow balls are 10% more than blue balls. Number of white balls is 15. Probability of choosing a red ball or a white ball is 13\/32.<\/p>\n\n\n\n
Based on the information given, answer the questions that follow:<\/p>\n\n\n\n
1) Some blue balls are transferred from bag A to bag B. If the balls were chosen at random, what is the probability of the weight of blue balls in B being at least 500g?<\/p>\n\n\n\n
A) 7\/12<\/p>\n\n\n\n
B) 3\/16<\/p>\n\n\n\n
C) 25\/76<\/p>\n\n\n\n
D) Cannot be determined<\/strong><\/p>\n\n\n\n E) 7\/76<\/p>\n\n\n\n Sol:<\/p>\n\n\n\n Weight of blue balls in the bag B before transfer<\/p>\n\n\n\n from bag A=18*20=360g<\/p>\n\n\n\n Weight of each blue ball is 20g and after transfer<\/p>\n\n\n\n the weight increases by (500g-360g) i.e.,140g<\/p>\n\n\n\n which is equivalent to the weight of 7 balls.<\/p>\n\n\n\n So, 7 balls must be transferred from A to B.<\/p>\n\n\n\n But we don\u2019t have any idea about how many<\/p>\n\n\n\n balls were transferred from A to B.<\/p>\n\n\n\n Thus, it cannot be discretely determined<\/p>\n\n\n\n 2) 6 balls were transferred from bag B to bag C while 10 balls were transferred from bag D to bag C. P is the probability of choosing a blue ball at random. What are the minimum and maximum possible values of P?<\/p>\n\n\n\n A) 7\/40, 3\/8<\/strong><\/p>\n\n\n\n B) 3\/16, 3\/8<\/p>\n\n\n\n C) 21\/80, 37\/80<\/p>\n\n\n\n D) 3\/80,27\/80<\/p>\n\n\n\n E) None of these<\/p>\n\n\n\n Sol:<\/p>\n\n\n\n For the minimum possible value of P, the case<\/p>\n\n\n\n must be that zero balls were transferred from<\/p>\n\n\n\n both bag B and bag D.<\/p>\n\n\n\n Also, after transfer of balls, total number of balls<\/p>\n\n\n\n in the bag=64+10+6=80<\/p>\n\n\n\n Minimum possible value of P=(no of blue<\/p>\n\n\n\n balls)\/total no of balls =14\/80=7\/40<\/p>\n\n\n\n For the maximum possible value of P, both 6<\/p>\n\n\n\n balls transferred from B and 10 balls transferred<\/p>\n\n\n\n from D must be blue in colour.<\/p>\n\n\n\n => Total number of blue balls after<\/p>\n\n\n\n transfer=14+6+10=30<\/p>\n\n\n\n Maximum possible value of P=30\/80=3\/8<\/p>\n\n\n\n 3) In bag C, all the red balls were marked an odd number against them starting from 1 while the yellow balls were marked an even number against them starting from 2. If one red ball and one yellow ball are chosen at random from the bag, what is the probability of getting a sum of numbers present on the balls more than 10?<\/p>\n\n\n\n A) 61\/63<\/strong><\/p>\n\n\n\n B) 9\/16<\/p>\n\n\n\n C) 7\/16<\/p>\n\n\n\n D) 62\/63<\/p>\n\n\n\n E) None of these<\/p>\n\n\n\n Sol:<\/p>\n\n\n\n In bag C, red balls=15 and they were marked<\/p>\n\n\n\n odd numbers 1,3,5,7,\u2026\u2026 while yellow balls=21<\/p>\n\n\n\n and they were marked even numbers<\/p>\n\n\n\n 2,4,6,8,10,\u2026\u2026\u2026<\/p>\n\n\n\n So, total number of outcomes=15*21=315<\/p>\n\n\n\n Outcomes giving sum of less than 10 are (1,2),<\/p>\n\n\n\n (1,4), (1,6), (1,8), (3,2), (3,4), (3,6), (5,2), (5,4), (7,2).Total number of outcomes with sum of<\/p>\n\n\n\n numbers less than 10=10<\/p>\n\n\n\n => Probability of getting sum of numbers less<\/p>\n\n\n\n than 10=10\/315=2\/63<\/p>\n\n\n\n Thus, probability of getting sum more than 10=1-<\/p>\n\n\n\n 2\/63=61\/63<\/p>\n\n\n\n 4) A man chose a ball at random from A and B each. What is the probability that the balls chosen have a combined weight more than 40g?<\/p>\n\n\n\n A) 15\/64<\/p>\n\n\n\n B) 5\/16<\/strong><\/p>\n\n\n\n C) 3\/8<\/p>\n\n\n\n D) 13\/64<\/p>\n\n\n\n E) None of these<\/p>\n\n\n\n Sol:<\/p>\n\n\n\n Weight of the red ball, blue ball, yellow ball and<\/p>\n\n\n\n white ball are 16g, 20g, 18g and 24g<\/p>\n\n\n\n respectively.<\/p>\n\n\n\n Since there are four colours and one ball from<\/p>\n\n\n\n each bag is chosen at random, total number of<\/p>\n\n\n\n outcomes=4*4=16<\/p>\n\n\n\n Let R, B, Y and W denote trails of choosing a<\/p>\n\n\n\n red, blue, yellow and white ball respectively.<\/p>\n\n\n\n For sum of weights to be more than 40g,<\/p>\n\n\n\n possible outcomes are BW, WB, WY, YW and<\/p>\n\n\n\n WW<\/p>\n\n\n\n Required probability=5\/16<\/p>\n","protected":false},"excerpt":{"rendered":" Direction: Read the following information carefully and answer the given questions: There are four bags A, B, C and D in which balls of different colours-red, blue, yellow and white are present. The weight of a red ball, a blue ball, yellow ball and a white ball are 16 g, 20 g, 18 g and […]<\/p>\n","protected":false},"author":419,"featured_media":162976,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[5138],"tags":[5139],"class_list":["post-162975","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-quantitative-aptitude","tag-quantitative-aptitude"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/162975","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=162975"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/162975\/revisions"}],"predecessor-version":[{"id":162977,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/162975\/revisions\/162977"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/162976"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=162975"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=162975"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=162975"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}