Solve this to get into MIT. 1876 admission test question

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MIT is one of the top ranked universities in the world. Can you solve this question from their 1876 admissions test?
Source
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Пікірлер: 788

@MaxMathGames 3 жыл бұрын

Was a challenging problem at that time but now, grade 7 and above students will be able to solve it. That's how, math has evolved

@warpromo6636 3 жыл бұрын

nah, hasn't really evolved. if the student knew systems of equations, but not the problem itself, they wouldn't have been able to solve it.

@warpromo6636 3 жыл бұрын

@insert username yea but if you gave a 12 year old that problem in the 1800's they wouldn't know how to solve it even if they knew systems of equations as it would've been an original problem not taught in schools

@PuzzleAdda 3 жыл бұрын

Watch this KZfaq video for the correct answer of this riddle. kzfaq.info/get/bejne/hMmih7p2md2baGg.html

@achyuththouta6957 3 жыл бұрын

@@warpromo6636 That doesn't make any sense. Once they knew that they can add and subtract equations they can solve it pretty easily. I knew how to add equations and I could do these by myself in seventh grade

@epikherolol8189 3 жыл бұрын

Actually class 6 students will solve it too

@ghotifish1838 3 жыл бұрын

When I heard it came from MIT I'm like wut this is so simple, but when I heard the year I was like ahh no wonder

@raman2192 3 жыл бұрын

Riddle: A father said to his son, Two years ago I was three times as old as you; but in fourteen years I shall be only twice as old as you. What were the ages of each? Answer - kzfaq.info/get/bejne/hMmih7p2md2baGg.html

@AKGSEP 3 жыл бұрын

1876 ;)

@achyuththouta6957 3 жыл бұрын

I mean this is simply about naming the variables and adding the equations. This is taught in grade 7.

@fargo1234 3 жыл бұрын

@@achyuththouta6957 see back in 1876 This might have been considered one of the hardest question

@ASAlan-sh8kf 3 жыл бұрын

I have a problem plz tell me can anyone help When Nabil's age was equal to Shubh's present age, Shubhar's age was twice that of Nabil's present age. When Shubhar's age is equal to Nabil's present age, what is the present age of each of them if the sum of the ages of the two of them is 63?

@ravirajamadan 3 жыл бұрын

A puzzle without Gogou's theorem is not a puzzle

@ackrige6175 3 жыл бұрын

Where them triangles at?

@PuzzleAdda 3 жыл бұрын

Watch this KZfaq video for the correct answer of this riddle. kzfaq.info/get/bejne/hMmih7p2md2baGg.html

@ashurawat1721 3 жыл бұрын

What is Gogous theorem

@mohamedbabe7324 3 жыл бұрын

🤣🤣🤣🤣

@wwoods66 3 жыл бұрын

@@ashurawat1721 It's what Mr. Tallwalker has taken to calling the Pythagorean Theorem, for ... reasons.

@TheManOfTomorrow 3 жыл бұрын

Indians outta nowhere: "We learnt solving this kind of problems before we learnt how to walk and talk."

@kajuskitchen 3 жыл бұрын

Yeah bro, I have been solving this type of problem since My class 6 days

@Aryan-iu4mv 3 жыл бұрын

12 and 13 year olds solve these questions easily in India. It's just simple equation what's so hard there. If you can understand the language of question and frame the correct equation it's a piece of cake.

@randomsahil 3 жыл бұрын

True that for 7th- 8th grade students

@santiagotheone 3 жыл бұрын

Yeah, this problem can be solved easily by most of the children in Asia when they are 12 or 13 years old.

@ayushmishra6687 3 жыл бұрын

In 10th or 9th grade we have done this

@sabyasachirimpa 3 жыл бұрын

Just imagine the brain power of Newton at that time. When MIT was asking a 7th grade math problem but Newton created formulas which even current generation can't grasp properly.

@popdop0074 2 жыл бұрын

@@RealNeelamPal Still is.

@dewangsingla1789 3 жыл бұрын

Now these kind of problems are taught in schools

@rahulpaul2119 3 жыл бұрын

Yes definitely

@terel9570 3 жыл бұрын

Not anymore

@epikherolol8189 3 жыл бұрын

In 6th class

@raman2192 3 жыл бұрын

@terel9570 3 жыл бұрын

@@raman2192 I watched a video like that before I watched this one. kzfaq.info/get/bejne/lbiHpttqzLvDiH0.html

@fhn_samin 3 жыл бұрын

I just realized I'm 18 and my father is 50. What a coincidence !!

@keinKlarname 3 жыл бұрын

@Farhan: Then I think two years ago your father was three times as old as you and in 14 years just two times.

@danmimis4576 3 жыл бұрын

so give your father this problem and you'll find out if he graduated MIT or is some high school dropout ...

@oktopg 3 жыл бұрын

@@danmimis4576 destroyed in seconds

@adw1z 3 жыл бұрын

Next year I’ll be 18 and my father will be 50 xDD

@rajkumartripathi1973 3 жыл бұрын

@@danmimis4576 Roasted!!!

@mattheweckermann535 3 жыл бұрын

Everyone is in the comment section flexing, bragging about doing this in grade school, and they don't seem to grasp the simple concept that this is from an admissions test into MIT not a part of the curriculum, meaning that it wouldn't be taught at the university but rather be expected that you already know how to do it. Plus, who's to say it isn't one of the easiest questions on the exam. In other words, congrats on being able to do something you were supposed to have been taught to do in school.

@kishoretejaswi1948 3 жыл бұрын

Well said!

@william2344 3 жыл бұрын

I know right why is it that everyone is flexing on this question but I never see them on all the other ones on this channel?. but anyway, this is very well said even if i was so close to getting it right ( got 46 for some reason)

@PuzzleAdda 3 жыл бұрын

Watch this KZfaq video for the correct answer of this riddle. kzfaq.info/get/bejne/hMmih7p2md2baGg.html

@kishoretejaswi1948 3 жыл бұрын

@@william2344 probably because you took the equation as X-2 = 3*Y in the first one. :) Honest mistake. Same here, first try from the thumbnail. Haven't watched the video.

@william2344 3 жыл бұрын

@@kishoretejaswi1948 thank you!

@GDLameGames 3 жыл бұрын

I was taught these types of problems in grade 8, but I still love solving them! Thanks Presh!

@madhukushwaha4578 3 жыл бұрын

Hii, If you want more harder questions then I will highly recommend you this channel's latest videos #onlymathlovers .

@raspberrieswithcream 3 жыл бұрын

This question is badly posed. It asks “What WERE the ages of each ?” The answer is that they WERE 48 and 16. If the question was instead “What ARE the ages of each” then the answer is that they ARE 50 and 18.

@parthpandya6412 3 жыл бұрын

Hmmm kinda makes sense tho

@AnssiRai 3 жыл бұрын

No, the whole narrative is in the past tense, ("A father said to his son..." etc.) and there never is a reference to the present time. Thus, the formulation ""What were the ages..." is the correct one. It refers to the time the father and son happened to have this conversation, which is some time in the past, but not at the present moment.

@parthpandya6412 3 жыл бұрын

@@AnssiRai you see the problem here is english doesn't have "past" and "more past" that's why that can be interpreted in both ways

@raspberrieswithcream 3 жыл бұрын

@@AnssiRai Well I think the question contains three different time zones, and hence needs three different tenses. I understand your reasoning but well-posed questions should not depend upon interpretation, unless of course the interviewer deliberately wants to wrong-foot the interviewee.

@AnssiRai 3 жыл бұрын

@@raspberrieswithcream and @Parth Pandya - the three tenses here would be: "how old were they [at the moment of the conversation]", "how old had they been [two years earlier" and "how old would they be [fourteen years later]"? None of these cases involve the present tense.

@ajhieb 3 жыл бұрын

Edit: My "shortcut" worked for this problem, but isn't actually a valid method, as noted below. This one was actually easy. I saw the thumbnail and figured it out on the way to the fridge. I used a slightly different approach. The time difference between 2x and 3x age is 16 years. (14+2) So that's x. So when the father was 3x the son's age (2 years ago) son was 16 and father was 48. Add 2 to each to and bingo, you have your current ages. Bingo.

@AkhilRoy7 3 жыл бұрын

same me also.. I solved before watch the video

@truth5030 3 жыл бұрын

But it should be 2(x+14)-3(x-2)=16 , what's your direct logic i can't understand brother.

@ajhieb 3 жыл бұрын

@@truth5030 my direct logic is a 16 year gap (14-(-2)) represents a change in relative ages from 2x to 3x. The difference between them (3x-2x) is x. So x=16. Now I know the age of the son 2 years ago when he was 1/3 the age of the father. Add 2 years to get his current age. The father was 3x 2 years ago, so take 3*16+2 and you get the father's current age of 50.

@PositronQ 3 жыл бұрын

Same but after I overcomplicated with other formula, was very easy

@GeorgeFoot 3 жыл бұрын

@@ajhieb Be careful, I think you've skipped a step. Your reasoning wouldn't work properly if the factors were 3x and 4x for example.

@helo3827 3 жыл бұрын

Bro, I wish the questions now are as easy as the questions from before.

@prafuldeosthale5016 3 жыл бұрын

Seconded

@tanmaybisht_iitbhu 3 жыл бұрын

But just like you, other participants will also be able to solve it very easily, then the competition will become even more tougher... don't u think so? 🤔🤔🤔

@shivrajanand2002 3 жыл бұрын

These questions were taught to us in 7 class in INDIA😂😂😂

@gauravtawri8803 3 жыл бұрын

Not in 1970s bro

@HackedPC 2 жыл бұрын

@@gauravtawri8803 right

@generousleo-7493 Жыл бұрын

exactly

@mathwithjanine 3 жыл бұрын

Loved this puzzle! :D

@n4p3r0 3 жыл бұрын

This was a simple one! Great video. :)

@madhukushwaha4578 3 жыл бұрын

Hii, If you want more harder questions then I will highly recommend you this channel's latest videos #onlymathlovers .

@swornthekillerintown 3 жыл бұрын

Before and really hated math but when I found your channel a really inspired me to understand math and now I'm a lot better at it I wouldn't say I'm great in it but I wouldn't say I'm terrible either

@okushitatsuhiro9936 3 жыл бұрын

【arithmetic】 father son gap two years ago ③ ① ② 　　　　　　　　　　　　　 ll in fourteen years ❷ ❶ ❶ therefore father son gap two years ago ③ ① ② 　　　　　　　　　　　　　 ll in fourteen years ④ ② ② ∴①＝2＋14 ＝16

@viniciusfernandes2303 3 жыл бұрын

Thanks for the video!!

@prayagtiwari4703 3 жыл бұрын

This was my maths book question of class 10th ncert 🤣🤣🤣🤣

@zzzzzz5411 3 жыл бұрын

Are you using ur schools email😂

@prayagtiwari4703 3 жыл бұрын

@@zzzzzz5411 no bro it's my personal email account actually I join the school class via using this id and teachers told use to write the class name that's why I do so. If you are a student you will understand.🤣🤣🤣🤣

@prayagtiwari4703 3 жыл бұрын

@@nelser1160 Bhai tereko kya hoa

@PuzzleAdda 3 жыл бұрын

Watch this KZfaq video for the correct answer of this riddle. kzfaq.info/get/bejne/hMmih7p2md2baGg.html

@anshbhilare9565 3 жыл бұрын

We get sums like this in class 10th lulw

@JaspreetSingh-dh4nf 3 жыл бұрын

Yeah.

@divyamgoyal774 3 жыл бұрын

Which are very easy....

@anshbhilare9565 3 жыл бұрын

@@divyamgoyal774 yep

@trax_edits 3 жыл бұрын

Yeassss

@diskritis2076 3 жыл бұрын

how are you guys preparing for boards?

@mo-oz8qr 3 жыл бұрын

That was easy thank you for hard working 😍

@jeaneltawil 3 жыл бұрын

WOOHOO! This was actually one I was able to solve on my own! I guess I'm better at these than at geometry :) Keep up the good work and happy holidays each and all

@madhukushwaha4578 3 жыл бұрын

😉 Hii, If you want more harder questions then I will highly recommend you this channel's latest videos #onlymathlovers .

@Neel-sama 2 жыл бұрын

Hi, even a 7th grader can solve it

@jeaneltawil 2 жыл бұрын

@@Neel-sama 😝

@gigachad2419 3 жыл бұрын

Congrats in Advanced MYD FOR 2M SUBS🤗❤🙏

@JoeBorrello 3 жыл бұрын

Well, they didn’t study quantum physics or relativity at MIT back then, so I guess this was appropriate for the time? Or maybe this was a sine qua non question to weed out the clueless.

@jimhood1202 3 жыл бұрын

They did study calculus however.

@olzenkhaw 3 жыл бұрын

This is the easiest question I found in this channel. This type of question I have been used it in my school exam.

@madhukushwaha4578 3 жыл бұрын

Hii, If you want more harder questions then I will highly recommend you this channel's latest videos #onlymathlovers ..

@deeptangshunathnath4668 3 жыл бұрын

Ah! I remember solving like these kind of father son ages question in class 6. But I liked the basicity of MIT

@IS-py3dk 3 жыл бұрын

Sir you asked exactly one of the quesrions that came in my 1st term exams

@jorghimvenerablebosstein7568 3 жыл бұрын

Nice fun simple problem! The way Presh aggressively said 50 at 2:14 made me laugh tho lol. 😂

@hrittikdhar1232 3 жыл бұрын

For the first time I solved a 'Mind Your Decision' problem before seeing the video.

@haysdixon6227 3 жыл бұрын

super funky that it’s MIT, guess it teaches you how much we’ve improved culturally at certain things over time now simultaneous equations are a super normal thing to do in middle/high school

@england1216 3 жыл бұрын

Lovely bit of simultaneous equations

@RangerCaptain11A 3 жыл бұрын

yippie! now i can go to MIT.

@nicholasharvey1232 Жыл бұрын

I thought of this puzzle as, for what pair of numbers-- in which the larger is 3 times the smaller-- does the larger become only two times as large when you add 16 to both. Naturally I tested on multiples of 16 first, and realized that in the earlier time, the son can be 16 and the father 48, while in the later time, the son is 32 and the father 64. So at the current time, son is 18 and dad is 50. It helps that I myself am 32 years younger than my own father. Indeed, my own father could have posed this riddle to me in 2002.

@vinceguemat3751 3 жыл бұрын

in order to simplifie one of the equation, i choose my varables being the age 2 years ago so the first one is juste x = 3y and the other one is x + 16 = 2 (y + 16) and we get y = 16 and x = 48 so when we add the 2 last years we also get 18 and 50

@vinceguemat3751 3 жыл бұрын

@@UTube4MNi also do it in my mind

@professoralvaromorte6233 3 жыл бұрын

That was easy... We learn to solve these sort of maths in primary schools in Bangladesh.

@leosinhoreto 3 жыл бұрын

I’m so happy I finally solved one 😁

@hellax968 3 жыл бұрын

It's the same aftab question from linear equation in two variables

@MaxMathGames 3 жыл бұрын

That's easily one of the easiest question on ages. But we'll explained ❤️❤️❤️👍👍👍

@zuregayeta7183 3 жыл бұрын

I got a riddle for you. If the father's age in 2020 is 25, his son's birthdate in the 25th of October, 2020; What will be the age of his son in the New Year of 2021?

@manoharsinghshekhawat9272 3 жыл бұрын

@@zuregayeta7183 2 months 6 days

@fiziwig 3 жыл бұрын

I'm used to being stumped by so many of his problems, but this was was trivial. :)

@madhukushwaha4578 3 жыл бұрын

Hii! You may have to visit this channel for more harder questions #onlymathlovers .

@jared4575 3 жыл бұрын

How I got the answer: I made it simpler by using “now” instead of “2 years ago” and “In 16 years” instead of “In 14 years” so I only had to keep track of the 16. Then I did a sample problem. Say they were 10 and 30, it would take 10 years for the father’s age to be only double of his son’s. I realize the starting sons age doubles until he is only double his fathers age, so I figured that the son had to be 16 and father had to be 48 two years ago, so I reached 18 and 50 by adding those years back

@michaelempeigne3519 3 жыл бұрын

I find it easier to make it one variable. 2 years ago: father = 3x and son = x Now : father = 3x + 2 and son = x + 2 14 years later : father = 3x + 16 and son = x + 16 since the father is only twice the son's age in 14 years, we can conclude that : 3x + 16 = 2 ( x + 16 ) 3x + 16 = 2x + 32 x = 16 substitute back into the Now equations and get : father = 50 and son = 18

@Aspirant-co2vg 3 жыл бұрын

Yep I did the same

@HereBeDragonsYT 3 жыл бұрын

I was able to do this one pretty easily in my head.

@thejdbechayda 3 жыл бұрын

First time I solved a problem from Mind Your Decisions 🙂🙂🙂

@madhukushwaha4578 3 жыл бұрын

Hii, If you want more harder questions then I will highly recommend you this channel's latest videos #onlymathlovers ....

@AmitSingh-qr2gg 3 жыл бұрын

Well the difference of ages will be same at any period, so a simple understanding of ratio can help to solve the problem in much less time

@vyneetwallah7728 3 жыл бұрын

You are just best!!

@madhukushwaha4578 3 жыл бұрын

Hii, If you want more harder questions then I will highly recommend you this channel's latest videos #onlymathlovers .

@wiellnyan 3 жыл бұрын

I hate these type of puzzled but it is good to learn.

@madhukushwaha4578 3 жыл бұрын

Hii, If you want more harder questions then I will highly recommend you this channel's latest videos #onlymathlovers ..

@PrashantYadav-dc1jb 3 жыл бұрын

So much easy this type of questions now ask in 5 th class

@madhukushwaha4578 3 жыл бұрын

Hii, If you want more harder questions then I will highly recommend you this channel's latest videos #onlymathlovers ....

@Shashwat712 3 жыл бұрын

Thank god! One problem that i have solved correctly from this channel😌😌(for Indians it was a easy one😁)

@anonymouse7640 3 жыл бұрын

I wish my school hire you as my maths teacher 😁😆

@SaintNine 3 жыл бұрын

Without watching the video, just reading the problem, I reasoned as follows: a-2=3(b-2) & a+14=2(b+14). We end up with a=3b-4 & a=2b+14, so 3b=2b+18, hence b=18 and a=50 substituting back into the first two equations: 50-2=3(18-2): 48=48 and 50+14=2(18+14): 64=64 it all checks out. Pretty straightforward.

@vedants.vispute77 3 жыл бұрын

Now little kids are allowed to subscribe this channel

@iamadityashekhar 3 жыл бұрын

We used to solve these type of riddles in Class 6-7th I wish MIT exam would have been like this only

@ac_ssc 3 жыл бұрын

I watched it carefully thinking that definitely I was missing something. 😆😆😆😆🤣🤣

@ArkSriva 3 жыл бұрын

Dude I did that orally just a little digit writing in the corner for memory

@TheHatkeHaryanvi 3 жыл бұрын

10th Class Question. Not at all hard problem, its very easier

@madhukushwaha4578 3 жыл бұрын

Hii, If you want more harder questions then I will highly recommend you this channel's latest videos #onlymathlovers .

@Sam_on_YouTube 3 жыл бұрын

I don't expect they wouldbhave thought students would fail to solve this puzzle. Rather, they were likely listening to them talk it through to get a sense of their speed and thought process.

@rajkumartripathi1973 3 жыл бұрын

This is only second time i solved ques of myd☺

@nachiketsomani1533 3 жыл бұрын

Human knowledge has increased so much in just 2 centuries. It never happened in last 1000s of years. The question that was considered extremely hard for mathematicians, is now asked in 8th class

@j.r.1210 3 жыл бұрын

Just because the question was on an MIT entrance exam in the 19th century doesn't mean it was considered "extremely hard for mathematicians" at the time. An entrance exam has to test some basic material too, such as the ability to create the proper equations to solve word problems. This could have been just one of 50 such questions. Moreover, people applying to MIT are high school students, not mathematicians.

@davidbgreensmith 3 жыл бұрын

Phew. One that I could do, for a change.

@diamondo7992 3 жыл бұрын

I really hope this is still the MIT entrance exam

@sree00667 3 жыл бұрын

Please make video on 2019 IMO Problem 6.

@etiennemarecaux6108 3 жыл бұрын

I did it in mind just looking at the miniature

@dpcubing1521 3 жыл бұрын

Me, who solved using substitution instead of elimination: Darn it, that took longer than it should’ve. Well at least I could solve ONE of these puzzles

@Artonox 3 жыл бұрын

wow shows how much more powerful math tools became. Were engineering concepts like matrices still struggling to make mainstream maths at the time?

@almighty97 3 жыл бұрын

At first sight it seemed to be very easy....but then i thought that if you made a video on this then it may have some difficulty.... but i was wrong it is as easier as it seems to be.

@madhukushwaha4578 3 жыл бұрын

Hii, If you want more harder questions then I will highly recommend you this channel's latest videos #onlymathlovers ..

@almighty97 3 жыл бұрын

Thanks for your recommendation Kushwaha ji

@kanishkagaggar 3 жыл бұрын

solution with only one equation: just equate expressions for father's age from both the relations. Ages 2 years back : x, 3x Ages 14 years from now: x+16, 2x +32 Thus : 3x + 16 = 2x + 32 => x = 16 => present ages : 18, 50...

@sonson-989 3 жыл бұрын

Well this one was easy. Woke up at 3 am with all my algebra skills off, was able to brutforce my way through this problem while I brushed my teeth.

@thej4468 3 жыл бұрын

I got 50 and 17ish(rounding) by just looking at ratios. Close enough. Makes since with the 2 years ago statement.

@happysahoo196 3 жыл бұрын

Why was the question is here ? What did I miss ?

@issbacademy 3 жыл бұрын

what are the ages of each I think?? not were

@michaelm4499 3 жыл бұрын

50 and 18 is the right answer, but not to the question asked. The question asks ‘what were the ages of each?’, emphasis on the were ie what were the ages of the father and son when the father was three times older than the son. The answer to that is 48 and 16. If the question was ‘what are the ages of each?’ then 50 and 18 would be correct because that is 2 years after the fact.

@MCAbdo 3 жыл бұрын

This is easy for me, my dad used to ask me tons of these as a kid 😂

@z4zuse 3 жыл бұрын

The challenge would be in the allowed time and whether paper is allowed.

@timburri5756 3 жыл бұрын

I don't get why he just subtracts the second equation from the first... somebody pls explain

@loredfolk1069 3 жыл бұрын

I did the equation part correctly, just didn’t know take swaying part

@dameongarouge5858 3 жыл бұрын

everybody knows practices but dosen't conceptually understand it by the method you can be better and topper but with practicing both is important

@AeroLowdown 3 жыл бұрын

Take the victories where you can

@TatsatMishra 3 жыл бұрын

I Have Studied It In Class 8th But Thanks Fod The Revision

@madhukushwaha4578 3 жыл бұрын

Hii, If you want more harder questions then I will highly recommend you this channel's latest videos #onlymathlovers ....

@davidwillis7991 3 жыл бұрын

Everyone loves to use two variables for a question like this but it's far easier to use a single variable.

@oo-ji8mv 3 жыл бұрын

'Age is just a number' would be perfect in this scenario

@kanishkagaggar 3 жыл бұрын

Some intersectional major studies would respond like that 😛

@mjlvnv 3 жыл бұрын

I came up with 30 and 10. Now I’ll watch the video to see if I right 😀

@robinlindgren6429 3 жыл бұрын

age of father: X age of son: Y equation (1): X-2 = 3(Y-2) equation (2): X+14 = 2(Y+14) simplify (1) to get (3): X = 3Y-4 use (3) to substitute out X in (2) and get (4): 3Y-4+14 = 2(Y+14) simplify (4) to get (5): Y = 18 use (5) to substitute out Y in (3) and get (6): X = 3*18-4 simplify (6) to get (7): X = 50 by (5) and (7) we have the solution: the father is 50 years old and the son is 18.

@Someone-vj2cz 3 жыл бұрын

68th yay I know it’s not as good as being 1st or 2nd or 3rd but I’m still contented

@gamingmusicandjokesandabit1240 3 жыл бұрын

1 million subs? You're 30K away from 2 million!

@bacteriajoe9403 3 жыл бұрын

I went with: f=2s f+16=2(s+16) solved for s and added 2 substituted in first for f and added 2 alternate explanation f=F-2 s=S-2 f=2s f+16=2(s+16) Solve for F and S

@irsabaku5044 2 жыл бұрын

Son: Dad how old are you ? Dad : Two years ago I was three times as old as you ; but in fourteen years I shall be only twice as old as you. Son : Whatever I dont need that !

@poisonousman7941 3 жыл бұрын

I did it mentally 😅 I think in India we hv these kind of que. in class 6,7,8 😅 but the que. is from 1876 😂😂😂 So thats ok 👍 I donot need to fly in air 😂

@yingo4098 3 жыл бұрын

Presh: can you solve it? me: yes! ah let's see here _gets calculus book_

@robxyz2926 3 жыл бұрын

I got caught up in interpreting the tense of the question. The Question states: what "were" the ages of each? It didn't say: What "are" the ages of each. So I took this to be the ages of the boy and his father 2 years ago. f=3s, f+2+14=2(s+2+14), f=48, s=16

@kamakshitrivedi8561 3 жыл бұрын

I can solve this problem in a simpler way by mere using ratios. 2 years ago the ratio between father's age and son 's age will be 3:1 and 14 years later it will be 2:1 But we all know that difference between age of 2 people never change. (if you are 3 years older than your brother then you will be 3 years older to him after 50 years also.) Here we have 2 stituations 1 1)Before 2 years the diff. Wwas 3-1=2 2)After 14 years the diff. will be 2-1=1 We need to equalize the diff so multiply 2 to 2 years ago ratio, i.e. 3:1)×2= 6:2 And multiply 4 to 14 years later ratio i.e. 2:1)×4=8:4 Now the diff is same in both the situations. Now the gap between both the years is 14+2=16 But in terms of ratio it is 2 units. This implies 2units=16 so 1unit=16/2=8. Thus, 2 years ago father's age was 6×8=48 years and son's age was 2×8=16. And 14 years later father's age will be 8×8=64 years and son's age will be 4×8=32. And Their present ages are 48+2=50 and 16+2=18.