{"id":90711,"date":"2025-06-01T10:35:05","date_gmt":"2025-06-01T10:35:05","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90711"},"modified":"2025-06-01T10:35:05","modified_gmt":"2025-06-01T10:35:05","slug":"the-average-age-of-father-and-elder-son-is-35-years-the-average-age-o","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-average-age-of-father-and-elder-son-is-35-years-the-average-age-o\/","title":{"rendered":"The average age of father and elder son is 35 years, the average age o"},"content":{"rendered":"

The average age of father and elder son is 35 years, the average age of father and younger son is 32 years and the average age of the two sons is 17 years. What is the average age of the father and his two sons?<\/p>\n

[amp_mcq option1=”30 years” option2=”27 years” option3=”28 years” option4=”29 years” correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2022<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nLet the age of the father be $F$, the elder son be $E$, and the younger son be $Y$.
\nGiven information:
\n1. Average age of father and elder son is 35 years: $(F + E)\/2 = 35 \\implies F + E = 70$.
\n2. Average age of father and younger son is 32 years: $(F + Y)\/2 = 32 \\implies F + Y = 64$.
\n3. Average age of the two sons is 17 years: $(E + Y)\/2 = 17 \\implies E + Y = 34$.<\/p>\n

We need to find the average age of the father and his two sons, which is $(F + E + Y)\/3$.<\/p>\n

Adding the three equations:
\n$(F + E) + (F + Y) + (E + Y) = 70 + 64 + 34$
\n$2F + 2E + 2Y = 168$
\n$2(F + E + Y) = 168$
\n$F + E + Y = 168 \/ 2 = 84$.<\/p>\n

The average age of the father and his two sons is $(F + E + Y)\/3 = 84\/3 = 28$ years.
\n<\/section>\n

\n– Understanding and setting up equations from average definitions.
\n– Solving a system of three linear equations with three variables.
\n– Calculating the final average.
\n<\/section>\n
\nWe can also find individual ages:
\n$(F+E+Y) = 84$
\nSubstitute $(E+Y)=34$: $F + 34 = 84 \\implies F = 50$.
\nSubstitute $F=50$ into $F+E=70$: $50 + E = 70 \\implies E = 20$.
\nSubstitute $F=50$ into $F+Y=64$: $50 + Y = 64 \\implies Y = 14$.
\nCheck with $E+Y=34$: $20 + 14 = 34$. The ages are 50, 20, and 14 years.
\nAverage age of father and sons = $(50 + 20 + 14)\/3 = 84\/3 = 28$.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

The average age of father and elder son is 35 years, the average age of father and younger son is 32 years and the average age of the two sons is 17 years. What is the average age of the father and his two sons? [amp_mcq option1=”30 years” option2=”27 years” option3=”28 years” option4=”29 years” correct=”option3″] … <\/p>\n

Detailed SolutionThe average age of father and elder son is 35 years, the average age o<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1085],"tags":[1108,1102],"class_list":["post-90711","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1108","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nThe average age of father and elder son is 35 years, the average age o<\/title>\n<meta name=\"description\" content=\"Let the age of the father be $F$, the elder son be $E$, and the younger son be $Y$. Given information: 1. Average age of father and elder son is 35 years: $(F + E)\/2 = 35 implies F + E = 70$. 2. Average age of father and younger son is 32 years: $(F + Y)\/2 = 32 implies F + Y = 64$. 3. Average age of the two sons is 17 years: $(E + Y)\/2 = 17 implies E + Y = 34$. We need to find the average age of the father and his two sons, which is $(F + E + Y)\/3$. Adding the three equations: $(F + E) + (F + Y) + (E + Y) = 70 + 64 + 34$ $2F + 2E + 2Y = 168$ $2(F + E + Y) = 168$ $F + E + Y = 168 \/ 2 = 84$. The average age of the father and his two sons is $(F + E + Y)\/3 = 84\/3 = 28$ years. - Understanding and setting up equations from average definitions. - Solving a system of three linear equations with three variables. - Calculating the final average.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/the-average-age-of-father-and-elder-son-is-35-years-the-average-age-o\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The average age of father and elder son is 35 years, the average age o\" \/>\n<meta property=\"og:description\" content=\"Let the age of the father be $F$, the elder son be $E$, and the younger son be $Y$. Given information: 1. Average age of father and elder son is 35 years: $(F + E)\/2 = 35 implies F + E = 70$. 2. Average age of father and younger son is 32 years: $(F + Y)\/2 = 32 implies F + Y = 64$. 3. Average age of the two sons is 17 years: $(E + Y)\/2 = 17 implies E + Y = 34$. We need to find the average age of the father and his two sons, which is $(F + E + Y)\/3$. Adding the three equations: $(F + E) + (F + Y) + (E + Y) = 70 + 64 + 34$ $2F + 2E + 2Y = 168$ $2(F + E + Y) = 168$ $F + E + Y = 168 \/ 2 = 84$. The average age of the father and his two sons is $(F + E + Y)\/3 = 84\/3 = 28$ years. - Understanding and setting up equations from average definitions. - Solving a system of three linear equations with three variables. - Calculating the final average.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/the-average-age-of-father-and-elder-son-is-35-years-the-average-age-o\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:35:05+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"The average age of father and elder son is 35 years, the average age o","description":"Let the age of the father be $F$, the elder son be $E$, and the younger son be $Y$. Given information: 1. Average age of father and elder son is 35 years: $(F + E)\/2 = 35 implies F + E = 70$. 2. Average age of father and younger son is 32 years: $(F + Y)\/2 = 32 implies F + Y = 64$. 3. Average age of the two sons is 17 years: $(E + Y)\/2 = 17 implies E + Y = 34$. We need to find the average age of the father and his two sons, which is $(F + E + Y)\/3$. Adding the three equations: $(F + E) + (F + Y) + (E + Y) = 70 + 64 + 34$ $2F + 2E + 2Y = 168$ $2(F + E + Y) = 168$ $F + E + Y = 168 \/ 2 = 84$. The average age of the father and his two sons is $(F + E + Y)\/3 = 84\/3 = 28$ years. - Understanding and setting up equations from average definitions. - Solving a system of three linear equations with three variables. - Calculating the final average.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/the-average-age-of-father-and-elder-son-is-35-years-the-average-age-o\/","og_locale":"en_US","og_type":"article","og_title":"The average age of father and elder son is 35 years, the average age o","og_description":"Let the age of the father be $F$, the elder son be $E$, and the younger son be $Y$. Given information: 1. Average age of father and elder son is 35 years: $(F + E)\/2 = 35 implies F + E = 70$. 2. Average age of father and younger son is 32 years: $(F + Y)\/2 = 32 implies F + Y = 64$. 3. Average age of the two sons is 17 years: $(E + Y)\/2 = 17 implies E + Y = 34$. We need to find the average age of the father and his two sons, which is $(F + E + Y)\/3$. Adding the three equations: $(F + E) + (F + Y) + (E + Y) = 70 + 64 + 34$ $2F + 2E + 2Y = 168$ $2(F + E + Y) = 168$ $F + E + Y = 168 \/ 2 = 84$. 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Given information: 1. Average age of father and elder son is 35 years: $(F + E)\/2 = 35 \\implies F + E = 70$. 2. Average age of father and younger son is 32 years: $(F + Y)\/2 = 32 \\implies F + Y = 64$. 3. Average age of the two sons is 17 years: $(E + Y)\/2 = 17 \\implies E + Y = 34$. We need to find the average age of the father and his two sons, which is $(F + E + Y)\/3$. Adding the three equations: $(F + E) + (F + Y) + (E + Y) = 70 + 64 + 34$ $2F + 2E + 2Y = 168$ $2(F + E + Y) = 168$ $F + E + Y = 168 \/ 2 = 84$. 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