Q. Age of R after 12 years is 80% more than present age of P, while present age of T is 20% more than S. Find the present average age of P and Q together<\/p>\n\n\n\n
Statement I: Present age of T is 80% more than P, while after 6 years age of Q is 50% as that of S.<\/p>\n\n\n\n
Statement II: R is 12 years older than Q, and the respective ratio of age of R and S after 4 years is 14:17.<\/p>\n\n\n\n
Statement III: P is 4 years younger than R and 8 years older than Q.<\/p>\n\n\n\n
A. Either I alone or II alone is sufficient to answer the question<\/p>\n\n\n\n
B. Either I alone or II and III together is sufficient to answer the question<\/p>\n\n\n\n
C. III alone is sufficient to answer the question<\/p>\n\n\n\n
D. Either III alone or I and II together is sufficient to answer the question<\/p>\n\n\n\n
E. None of these<\/p>\n\n\n\n
Ans: Either III alone or I and II together is sufficient to answer the question<\/p>\n\n\n\n
sol:<\/p>\n\n\n\n
(R + 12) \/ P = 9\/5<\/p>\n\n\n\n
5R + 60 = 9P<\/p>\n\n\n\n
9P \u2013 5R = 60\u2026\u2026\u2026\u2026\u2026… (1)<\/p>\n\n\n\n
T\/S = 6\/5\u2026\u2026\u2026\u2026\u2026 (2)<\/p>\n\n\n\n
From Statement I,<\/p>\n\n\n\n
T\/P = 9\/5<\/p>\n\n\n\n
So, T:S:P = 18:15:10 [18a, 15a, 10a]<\/p>\n\n\n\n
(Q + 6) \/ (S + 6) = 1\/2<\/p>\n\n\n\n
2Q + 12 = S + 6<\/p>\n\n\n\n
S \u2013 2Q = 6<\/p>\n\n\n\n
Q = (S \u2013 6)\/2 = (15a \u2013 6)\/2<\/p>\n\n\n\n
This statement alone is not sufficient to answer<\/p>\n\n\n\n
the question<\/p>\n\n\n\n
From Statement II,<\/p>\n\n\n\n
R = 12 + Q<\/p>\n\n\n\n
(R + 4) \/ (S + 4) = 14\/17<\/p>\n\n\n\n
17R + 68 = 14S + 56<\/p>\n\n\n\n
14S \u2013 17R = 12<\/p>\n\n\n\n
This statement alone is not sufficient to answer<\/p>\n\n\n\n
the question<\/p>\n\n\n\n
From Statement III,<\/p>\n\n\n\n
R \u2013 P = 4<\/p>\n\n\n\n
Also, we have<\/p>\n\n\n\n
9P \u2013 5R = 60<\/p>\n\n\n\n
On adding both equations, we get<\/p>\n\n\n\n
4R = 96
Age of R = 24 years
Age of P = 24 \u2013 4 = 20 years
Age of Q = 20 \u2013 8 = 12 years
Required average = (20 + 12)\/2 = 16 years
This statement alone is sufficient to answer the
question
On combining Statement (I + II),
Q = (15a \u2013 6)\/2
R = 12 + (15a \u2013 6)\/2 = (18 + 15a)\/2
S = 15a
Also,
14S \u2013 17R = 12
So,
14 x 15a \u2013 17 x (18 + 15a)\/2 = 12
Value of a = 2
So, age of Q = (15 x 2 \u2013 6)\/2 = 12
Age of P = 10 x 2 = 20
Required average = (20 + 12)\/2 = 16 years
This combination is sufficient to answer the
questions.
Either I and II together or III alone is sufficient to
answer the question.
Hence answer is option D<\/p>\n","protected":false},"excerpt":{"rendered":"
Q. Age of R after 12 years is 80% more than present age of P, while present age of T is 20% more than S. Find the present average age of P and Q together Statement I: Present age of T is 80% more than P, while after 6 years age of Q is 50% […]<\/p>\n","protected":false},"author":419,"featured_media":162671,"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-162670","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\/162670","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=162670"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/162670\/revisions"}],"predecessor-version":[{"id":162672,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/162670\/revisions\/162672"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/162671"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=162670"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=162670"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=162670"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}