 Hello friends welcome to this video session on word problem solving and so far we have solved a couple of problems on how to find out hcf or gcd of two positive integers using Euclid's division algorithm. We also saw how to express gcd of two given positive integers as a linear combination of the two numbers as well as we saw that the linear combination so obtained was not unique. In this session we have taken one exercise problem which is you know commonly what you call as a word problem and this has been picked up from ncrt book and we'll try to solve this problem using the relevant concepts and we'll also try to understand what should be the approach of solving such word problems because in my experience I have seen students struggling to interpret the problem in the first place and then convert the word problem into relevant mathematical equations and hence solve the problems but let us try and understand how it is done and also try to form a methodology so that you can adopt this methodology every time you encounter word problems. So let us start with you know breaking down the question. What is the question so question says a contingent of 616 members so it's always a good practice to highlight the data which is given in the question paper because I have seen many people take down the questions itself wrongly so you know highlight the data point so contingent of 616 members is to march behind an army band of 32 members so there will be a band of a band of 32 members here followed by a contingent of contingent of 616 members the two groups are to march in the same number of columns that means the same number of columns as if you have seen Republic Day parade or any other parade which happens in your school if you see there are columns in which the contingent marches right so what they're saying is the two groups are to march in the same number of columns that means the army band will be followed by the contingent and the number of columns is same number of columns is same okay and now we have to find out what is the maximum number of columns maximum so this is what is the keyword we are looking for this keyword now the moment you know one you know thumb rule normally you know is very common by solving such problems is the moment you say maxi maximum then one thing which should come to your mind obviously you have to have the context of the problem where you are dividing two numbers into into some equal equal equal sized groups right what we saw in our division algorithm if you saw in the first few sessions if you have not seen that I would recommend you go and watch those sessions as well so here maximum maximum means the moment this word comes so one thing which should strike our mind is hcf why because h is highest and which is you know resonating with maximum hcf or gcd greatest common divisor so somehow it indicates it did not mean necessary my friends please mind it it did not mean necessary the problem involves the you know the concept of hcf and gcd but it gives me an idea that okay it might be that so hence we will try and see if that is applicable okay so clearly if you if you draw a representative diagram so you have a contingent here you have another contingent here and you have to divide them into equal number of columns same number of columns and each column has to have maximum number of people so clearly this is nothing but dividing or finding the highest common factor of 32 and 616 because if we find out the highest common factor then so that will be the number of people in one group and you can find out the number group of groups as well so hence it boils down that we have to find out the hcf or gcd gcd of what 616 616 and 32 now if the question doesn't categorically mention which which method of finding gcd is to be adopted then you can find out either using long division method if you know this is the way we have been finding out hcf long division method or you can adopt if they are categorically mentioning then you have to use something called Euclates Euclates division algorithm which we have seen in the previous few sessions sessions and or you know the prime factorization method whichever prime factorization method so whichever method you feel like you can adopt it and use to solve the problems so once again clearly I have to since I have to divide 616 and 32 into some number of people so let's say 16 each if I have to if one in one column if I am dividing it into two columns then I will be having 600 and sorry 16 people in two columns here and if let's say that number of columns has to be same because the question demands it so hence if I keep two columns here 600 you know two columns here then the number of people here in one column will be 308 clearly but then this is not the maximum number of columns actually I can go for four column also or you will see what is the maximum number of such columns how do I find out that number of columns clearly by finding the gcd out okay so let's start and find out gcd I'll be adopting Euclates division algorithm so let us use Euclates division algorithm to find out the hcf so 616 will be written at as a now the device at first b is 30 and this item I don't know we'll have to find out what it should be and q and r have to be found out now in such cases how do I find out so 32 how many times 32 goes into 616 either you can do a quick calculation on you know you can do the quick calculation by you know finding out the quotient and remainder so if you see 30 32 goes one times 232 and then here it is how much um this is 29 right so 296 is my this thing so obviously 32 10 times will be 320 so it has to be one less so let's say 19 times clearly 19 times 32 will be how much uh let's see uh so it is nine times two that is 18 and 127 288 so if you see what is the remainder eight isn't it so if you don't know then you can do that or you can also find out through long division method whichever method suits you now so hence what do I what do I see it is 32 into 19 and then plus eight remainder right the next step is the b becomes a so 32 comes here and r becomes b so eight comes here now luckily we got it a into 4 is 32 plus 0 as the remainder so thankfully by grace of god we are not going to do this process uh now you know any further so in the two steps itself I know the gct is eight okay so hence the answer would be eight so if you divide 32 and 616 in in columns of eight that's the maximum number of columns you will get such that the number of people in each column is same so that means the army band of 32 the army band of 32 divided by eight that means in each column you'll get four people so four four of four people in each column and such such eight columns followed by 616 by eight which is how much if you see it is nothing but eight seven times goes right seven and then 77 if you see 56 and then 50 seconds 77 so in in uh you know so hence what will happen is there will be eight columns and there will be four files like that so for for the for the army band isn't it like that so there will be eight eight such columns so column number one column number two three four five and so on and so forth and there will be four such rows okay four such rows and here 77 such rows will be there for the other contingent and divide into eight columns like that so this is how the contingent will be formed and they will march in the parade so that was the question so again reemphasizing the keyword was highest here and that highest indicated that we should evaluate whether hcf or gcd concept could be utilized here so i hope you understood the problem and for more problem solving sessions please subscribe to our channel you'll get more such questions in sort form thanks a lot for watching this video