Mathematics... the king of them all!

by **The Prince** » Fri Mar 28, 2003 8:14 pm

Hi friends, why not try solving some puzzles and problems pertaining to mathematics? Let us post some problems/puzzles and test/analyze ourselves. Anyone having a flair for maths are welcome. But one request... please do not post comments questioning the purpose of this board, okay?

by **The Prince** » Fri Mar 28, 2003 8:19 pm

First question - on a river of width 54 meters, there are 2 planks comprising a drawbridge. The planks are in such a way that they are overlap for 2 meters (common area = 2m). If both these planks rise to an angle of 60 degrees, what is the width of passage available for a boat to pass by?

by N » Sat Mar 29, 2003 9:55 am

Mr. Prince, first things first - the units of area are length square and not length...

by N » Sat Mar 29, 2003 9:59 am

Should I assume that both the planks are of same size ? You didn\'t mention anything abt this... If so, why should I assume that? I think for such things, Sakuntala Devi puzzle book available in most book stores are good.

by **The Prince** » Tue Apr 01, 2003 2:19 pm

Mr. N .. sorry for that dimensions part. that was meant to say that the planks had an overlapped or common length of 2 meters. and coming to size of the planks .. it is in no way required to solve the prob. that will be absolutely unneccesary info if the planks are of the same size or not. u need not assume any thing. and this is not a shakunthala devi question. it is from JEE-2001 paper. better luck.

by **krishna chaitanya** » Tue Apr 01, 2003 7:11 pm

May I know what you mean by a 60 degree rise? Is this the angle with the vertical or with the horizontal?

by **The Prince** » Tue Apr 01, 2003 10:24 pm

60 degrees with the horizontal.

by **Raghu** » Wed Apr 02, 2003 11:42 pm

54 - 28 * sqrt(3)

by **The Prince** » Thu Apr 03, 2003 12:40 pm

sorry boss... that is wrong. check out that sqr(3) part. cosine angle.

by **Raghu** » Thu Apr 03, 2003 11:48 pm

Darn it. My trig is so rusty that I thot cos 60 was sqrt(3)/2. anyways, the answer i think is 54 - 28 cos 60 = 40,

by **The Prince** » Fri Apr 04, 2003 9:01 am

here\'s the answer. each plank\'s length accounts to 28 m. now when the draw bridge raises through 60 degrees, a total of 28*cos(60)=28*1/2=14 m gets reduced in the passage. as there are two planks, the total passage of 54 m gets reduced to 54-2(14) i.e= 26m is the passage left.

by N » Fri Apr 04, 2003 11:30 am

y did u assume that both planks are 28 mts ???

by N » Fri Apr 04, 2003 11:36 am

it can be anythin, not only 28 mts, when x+y=56 and xcos60+ycos60+gap=54, the answer always is 26 irrespective of what x or y is right ?? what is so IIT abt it ? not even worth an for an EAMCET bit question. may be one mark question for tenth class heights and distances.

by N » Fri Apr 04, 2003 11:44 am

a question from ragging time, write ur rank in the form (xpowery + ypowerx) pretty simple.

by **The Prince** » Fri Apr 04, 2003 12:57 pm

Mr. N, why do you assume those things? Why 28? Why same length? For a drawbridge to open, the planks open up from the centre and as the width of river is 54 m... the length of each plank is 26 + common length (2) = 28 m. When you know that xcos60 + ycos60 + gap = 54, where does 26 come from? And if this is a Std X one mark bit, why didn\'t you get it?

by **Kishore** » Fri Apr 04, 2003 5:59 pm

That would be 1powerx + xpower1 where x = rank - 1...

Who is online