Q. Time taken by boat to travel (K + 175) km upstream is 50% more than time taken by boat to travel (K + 250) km downstream. Speed of the boat in still water is four times the speed of the stream.<\/p>\n\n\n\n
Find which of the following statement(s) is\/are true.<\/p>\n\n\n\n
I. Time taken by boat to travel (2K \u2013 80) km downstream is 184\/3 hours. Speed of stream is 3 km\/h<\/p>\n\n\n\n
II. Time taken by boat to travel (K \u2013 140) km upstream is twice of time taken by boat to travel (K\/2 + 50) km downstream<\/p>\n\n\n\n
III. Unit digit of (K\/4 + 4)99 is 9<\/p>\n\n\n\n
A. II only<\/p>\n\n\n\n
B. III only<\/p>\n\n\n\n
C. I and II only<\/p>\n\n\n\n
D. II and III only<\/p>\n\n\n\n
E. None of these<\/p>\n\n\n\n
Ans: None of these<\/p>\n\n\n\n
Sol:<\/p>\n\n\n\n
Let speed of stream = a
So, speed of stream in still water = 4 x a = 4a
Now,
[(K + 175) \/ (4a \u2013 a)] \/ [(K + 250) \/ (4a + a) = 3\/2<\/p>\n\n\n\n
10K + 1750 = 9K + 2250
Value of K = 500
I. Time taken by boat to travel (2K \u2013 80) km
downstream is 184\/3 hours. Speed of stream is
3 km\/h
Downstream speed of boat = 3 + 3 x 4 = 15 km\/h
Distance to travel = 2 x 1000 \u2013 80 = 920 km
Required time = 920\/15 = 184\/3 hours
This statement is true
II. Time taken by boat to travel (K \u2013 140) km
upstream is twice of time taken by boat to travel
(K\/2 + 50) km downstream
Respective ratio of upstream distance and
Downstream distance travelled = (500 \u2013 140):
(500\/2 + 50) = 6:5
Ratio of upstream speed and Downstream
speed respectively = (4 \u2013 1): (4 + 1) = 3:5
Ratio of upstream time and Downstream time =
6\/3: 5\/5 = 2:1
This statement is true
III. Unit digit of (K\/4 + 4)99 is 9
(K\/4 + 4) = 129
91 = 9
92 = 1
93 = 9
So, odd power of 9 gives 9 as a unit digit
So, required unit digit = 9
This statement is true
All statement(s) is\/are true
Hence the answer is option E<\/p>\n","protected":false},"excerpt":{"rendered":"
Q. Time taken by boat to travel (K + 175) km upstream is 50% more than time taken by boat to travel (K + 250) km downstream. Speed of the boat in still water is four times the speed of the stream. Find which of the following statement(s) is\/are true. I. Time taken by boat […]<\/p>\n","protected":false},"author":419,"featured_media":162674,"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-162673","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\/162673","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=162673"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/162673\/revisions"}],"predecessor-version":[{"id":162675,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/162673\/revisions\/162675"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/162674"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=162673"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=162673"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=162673"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}