This one is slightly easier to understand.
Since they completed the work together, time spent by both on the job is same.
Thus, remuneration paid to them should be in the ratios of the work they've done.
Ratio of work done by Apurva to Amit = 54/81=2/3
Now, suppose total work be 5x
Apurva does 5x in 12 days. Therefore, she'll do her part which is 2x in (12/5x)*2x = 24/5 days.
@rk90 said: @Nil253259:yes.hw?i guess itz really simple.bt still cant gt it.plz explain.
@rk90 said: raju is twice as good as vijay.together,they finish the work in 14 days.in how many days can vijay alone do the same work?approach plz.
I guess converting all integers in standard form will do the trick.
This is how I did it.
log 242 =a
log 80 = b
log 45 = c
log 36 = ?
log 36 = log (2^2 x 3^2) or log 2^2 + log 3^2 (1)
log 45 = log 3^2 + log 5 = c
= log 3^2 + log (5x2) - log 2
=log 3^2 + log 10 - log 2
log 3^2 = c - log 10 + log 2
Putting the value of log3^2 in (1)
=log 2^2 + c - log 10 + log 2
=log 2^3 - log 10 + c
From log 80
log 2^3 = b - log 10
With the value of log 2^3, we get
log 36 = b - log 10 - log 10 + c
=b + c - 2
@Fuhgetaboutit said: If log 242 = a , log 80 = b, log 45 = c Express log 36 in terms of a, b and c All values are to the base 10.Can someone tell me how to approach such a type of problem.
17^2=289>275
19^2=361
Therefore, option b is true.
@[586108:Fuhgetaboutit]
I haven't used it because I found it redundant in the question. This is evident from the options as well (no 'a' in options).
As far as finding the correct option is concerned, put a =1, b=2 & c=3 in the answer I got & do the same with the options.
You get 3rd as the right answer with the integral value 3
@[586108:Fuhgetaboutit]
Option b is correct.
Solution : -
'log 275 to the base 17 = x' means what power(x) should I raise 17 to so that I get 275. x can only be less than 2 since 17^2 is 289. On the other hand, log 375 to the base 19 attains a value greater than 2.
Hence, b is the right option.
@pradeeprai said:@rk90........
total work (lcm of individual time to do work) 2*x*xindividual days .................................... efficiencyraju= x ...................................................2*xvijay= 2*x............................ x..........................................................................sum =3*xnow the no of days taken by both = total time /total efficiency of them= 2*x*x/3*x=14(given). . x=21 and no of days by vijay = 2*21=42
A couple of questions from remainder:
@buffon said:A couple of questions from remainder:
1. Remainder(2^32/641)2. Remainder(11^97/77) - Here, i am not so clear about how to get past the 11/11*(7k+1)/7 stage..
@abhishek-c said:Just began solving Arun Sharma and here are some questions I couldn't solve.Number Systems LOD-IQ19. Find the number of zeroes at the end of 1090!(a) 270 (b) 268 (c) 269 (d) 271Q27.There are 576 boys and 448 girls in a schools that are to be divided into equal section of either boys or girls alone.Find the total number of sections formed.(a) 24 (b) 32 (c) 16 (d) 20 (e) None of theseQ47. Find the number of divisors of 10800.(a) 57 (b) 60 (c) 72 (d) 64 (e) None of these
@[513192:abhishek-c] refer quantum cat : unit 1 fundamentals ,u can solve these
@pradeeprai said: @abhishek-c refer quantum cat : unit 1 fundamentals ,u can solve these19) it can be solved by finding greatest power of 5 in 1090 ie., by prime factorization of 1090 by 5 and adding up all the quotients u get 218+43+8=270so,option a47)prime factorization again u get 2^4*3^3*5^2 => and now add 1 to the powers and multiply =>5*4*3 =60q 27) @Budokai001 i didn't get you ,could u plz elaborate it??
@[584723:bindita] ok.i got it ......thank u 😃
can someone tell me how to solve these please?
1)Find the lcm of (x+3)(6x^2+5x+4) and (2x^2+7x+3)(x+3).
Ans: (4x^2-1)(x+3)(3x+4)
2)The HCF of 2472,1284 and a 3rd no N is 12.If their LCM is 2^3*3^2*5*103*107, then find the no N.
Ans: The answer given is 4*9*5, but using hcf*lcm= product of nos, i get 15 as the answer.
3)Find the no of zeros at the end of 77! * 42!.
Ans: The answer given is 27 but im getting a different answer.
4)Can we find the remainder of 51^203 when divided by 7 without using the pattern method at all?
5)The book says a^n/a+1 leaves a remainder of a if n is odd and 1 if n is even.How can this be true? Shouldnt it be the other way round?
6)3 Mangoes, 4 guavas and 5 watermelons cost rs 750. 10 watermelons , 6 mangoes and 9 guavas cost Rs 1580.What is the cost of 6 mangoes, 10 watermelon and 4 gauvas.
Ans:1180
7)Least no by which 12,15,18,20 when divided leaves a remainder of 4 in each case. Shouldnt the answer be 4 itself?
8)A boy took a 7 digit no ending in 9 & raised it to an even prime no >2000.He then took the no 17 and raised it to a power which leaves the remainder 1 when divided by 4,if he now multiplies both the nos, what will be the units digit of the no he so obtains.
Ans:7
9)If AB+XY = 1XP, where A not = to 0 & all the letters signify different digits from 0 to 9, find the value of A.
Ans:9
10)3 nos are such that the second is as much lesser then the 3rd as the first is lesser than the second. If the product of the 2 smaller nos is 85 and the product of the 2 larger nos is 115, find the middle no.
Ans:10
11)Find 2 3 digit nos whose sum is a multiple of 504 & the qyuotient is a multiple of 6.
Ans:144,864
12)Define a number K such that it is the sum of the squares of the first M natural nos where M
Ans:12
Pals can any one please expain me this problem with explanation
*)A mother distributes 5 different apples among 8 children.
(i) How many ways can this be done if each child recieves at most one apple?
(a) 8.7.6 (5!)
(b) Other
(ii) How many ways can this be done if there is no restriction on the number of apples a child can recieve?
(a) 5^8
(b) Other
@macintosh2012 said:Pals can any one please expain me this problem with explanation
*)A mother distributes 5 different apples among 8 children. (i) How many ways can this be done if each child recieves at most one apple?(a) 8.7.6 (5!) (b) Other(ii) How many ways can this be done if there is no restriction on the number of apples a child can recieve?(a) 5^8 (b) Other
@greenpastures said: can someone tell me how to solve these please?1)Find the lcm of (x+3)(6x^2+5x+4) and (2x^2+7x+3)(x+3).Ans: (4x^2-1)(x+3)(3x+4)2)The HCF of 2472,1284 and a 3rd no N is 12.If their LCM is 2^3*3^2*5*103*107, then find the no N.Ans: The answer given is 4*9*5, but using hcf*lcm= product of nos, i get 15 as the answer.3)Find the no of zeros at the end of 77! * 42!. Ans: The answer given is 27 but im getting a different answer.4)Can we find the remainder of 51^203 when divided by 7 without using the pattern method at all?5)The book says a^n/a+1 leaves a remainder of a if n is odd and 1 if n is even.How can this be true? Shouldnt it be the other way round?6)3 Mangoes, 4 guavas and 5 watermelons cost rs 750. 10 watermelons , 6 mangoes and 9 guavas cost Rs 1580.What is the cost of 6 mangoes, 10 watermelon and 4 gauvas.Ans:11807)Least no by which 12,15,18,20 when divided leaves a remainder of 4 in each case. Shouldnt the answer be 4 itself?8)A boy took a 7 digit no ending in 9 & raised it to an even prime no >2000.He then took the no 17 and raised it to a power which leaves the remainder 1 when divided by 4,if he now multiplies both the nos, what will be the units digit of the no he so obtains.Ans:79)If AB+XY = 1XP, where A not = to 0 & all the letters signify different digits from 0 to 9, find the value of A.Ans:910)3 nos are such that the second is as much lesser then the 3rd as the first is lesser than the second. If the product of the 2 smaller nos is 85 and the product of the 2 larger nos is 115, find the middle no.Ans:1011)Find 2 3 digit nos whose sum is a multiple of 504 & the qyuotient is a multiple of 6.Ans:144,86412)Define a number K such that it is the sum of the squares of the first M natural nos where M2) hcf*lcm=product of nos. is applicable for two numbers only,not more than that.Follow the basic method of factorisation.3) no.of zeroes in 77!=15+3=18 and in 42! is 8+1=9. So total=18+9=27.4) {51^203/7} = {2^203/7}..{} represents remainder2^3 gives a remainder 1 on division by 7 and 2^203 =2^201*2^2..so remainder=45) follow the basic method,you won't need this formula.6)double the 1st equation and subtract it from the 2nd.You'll get the cost of 1 guava..Now proceed.7) the question is least number "by which" 12,15 etc are divided,not least no."which when divided by" 12,15 etc..However,it should have been "which when divided by".8) How can an even number>2000 be prime.?. the number should be either even or prime.9 raised to any even power ends in 1..the power to which 17 is raised in of the form 4k+1,hence unit digit of the power=7 (follow cyclicity rules). so answer=1*7=79) Should go by the options i guess.10) the numbers are in AP,so take them as x-d,x and x+d..form 2 sets of equations and solve.11)back-calculate from the options. This will save your time as well.12) k=n*(n+1)*(2n+1)/6..now 2n+1 is always odd,so not divisible by 4.either n or n+1 should be divisible by 8 (here n=M..:P) since 6 already contains a factor 2.number of multiples of 8 less than 55=6,so answer 12..phew,too many questions at 1 go..
There are 4 identical oranges, 3 identical mangoes and 2 identical apples in the basket. the number of ways in whihc we can select one or more fruits from the basket is
Ans:60, 59, 57, 55, 56
Please help in solving this