"Four athletes run a race, starting from the same point and all of them running clockwise. If the ratio of the speeds of the athletes are 1:2:3:4, at how many distinct points on the circular track will the two athletes meet?"
@veertamizhan said:"Four athletes run a race, starting from the same point and all of them running clockwise. If the ratio of the speeds of the athletes are 1:2:3:4, at how many distinct points on the circular track will the two athletes meet?"
4???
@Cat.Aspirant123 said:Suzie covers 700 kms in 9 hours out of which she covers 300 kms by bus and remaining by car.She takes 20 mins more if she covers 500 kms by bus and remaining by car. Find the ratio of thespeeds of bus and car.
300/x+400/y=9
500/x+200/y=28/3
700/x=29/3
x=2100/29
y=1400/17
x:y=21*17/(14*29)
x:y=51/58
@veertamizhan said:"Four athletes run a race, starting from the same point and all of them running clockwise. If the ratio of the speeds of the athletes are 1:2:3:4, at how many distinct points on the circular track will the two athletes meet?"
4 points
L,L/2,L/3,2L/3
@veertamizhan said:"Four athletes run a race, starting from the same point and all of them running clockwise. If the ratio of the speeds of the athletes are 1:2:3:4, at how many distinct points on the circular track will the two athletes meet?"
Speeds are x, 2x, 3x, 4x
Person 1 and 2 meet at points (2pi)
Person 1 and 3 meet at points (pi), (2pi)
Person 1 and 4 meet at points (2pi/3), 2*(2pi/3), (2pi)
Person 2 and 3 meet at points (2pi)
Person 2 and 4 meet at points (pi), (2pi)
Person 3 and 4 meet at points (2pi)
So, it should be 4 points (pi, 2pi, 2pi/3, 4pi/3)
Which are the 6 points the book mentions ?
"In a race between A and B, both start simultaneously from the same point but A runs clockwise and B runs anticlockwise. They meet for the first time at a distance of 300 meters clockwise from the starting point and for the second time at a distance of 200 meters anticlockwise from the starting point. Find the ratios of speeds of A and B, if it is known that A has not completed one full round until the second meeting."
@veertamizhan said:"In a race between A and B, both start simultaneously from the same point but A runs clockwise and B runs anticlockwise. They meet for the first time at a distance of 300 meters clockwise from the starting point and for the second time at a distance of 200 meters anticlockwise from the starting point. Find the ratios of speeds of A and B, if it is known that A has not completed one full round until the second meeting."
5/3???
@veertamizhan said:@ashish100 yes. please explain.
bhai let length of whole circle is d then
d-300/300 = vb/va
d+200/d-200=vb/va
solve
d=800
and vb/va=5/3
A manufacture estimates that on inspection 12% of the articles he produces will be
rejected.He accepts an order to supply 22000 articles at Rs 7.50each.he estimates the profit on his outlay including the manufacturing of rejected articles to be 20%.
Find the cost of manufacturing each article.
a.rs 6 b.rs 5.50 c.rs 5 d.rs 4.50
@IIM-A2013 said:A manufacture estimates that on inspection 12% of the articles he produces will be rejected.He accepts an order to supply 22000 articles at Rs 7.50each.he estimates the profit on his outlay including the manufacturing of rejected articles to be 20%. Find the cost of manufacturing each article. a.rs 6 b.rs 5.50 c.rs 5 d.rs 4.50
0.88*22000 =19360
(19360*7.5 -22000*x )/(22000*x) =0.20
x=5.5
@IIM-A2013 said:A manufacture estimates that on inspection 12% of the articles he produces will be rejected.He accepts an order to supply 22000 articles at Rs 7.50each.he estimates the profit on his outlay including the manufacturing of rejected articles to be 20%. Find the cost of manufacturing each article. a.rs 6 b.rs 5.50 c.rs 5 d.rs 4.50
0.20x=.88*7.5-x
x=5.5
x=5.5
Do there exist 10 distinct integers such that the sum of any 9 of them is a perfect
square.?
square.?
Pardon me for posting the question with no knowledge of the answer...
Find all nonnegative integers n such that there are integers a and b with the property
n^2 = a + b and n^3 = a^2 + b^2.
@ScareCrow28 said:Do there exist 10 distinct integers such that the sum of any 9 of them is a perfectsquare.?Pardon me for posting the question with no knowledge of the answer...
There would be many such sets of 10 integers.
Take any 10 multiples of 3 (say a1,a2,a3.......a10)
Say the sum of the squares of these numbers is S
now you can generate 10 distinct integers using formula
Xi = S/9 - ai^2
These ten integers generated will satisfy the required conditions.
One such set of integers is.
376.00
349.00
304.00
241.00
160.00
61.00
-56.00
-191.00
-344.00
-515.00
349.00
304.00
241.00
160.00
61.00
-56.00
-191.00
-344.00
-515.00
ATDH.
@naga25french said:I think answer is just 1a,b should be 1,0 or 0,1
Sir, number of values of "n" niklna hai
@naga25french said:even in that case n can take value of 1 ..A number N can be expressed as sum of 2 squares if and only if every prime in N of the form (4k+3) occurs an even number of times .I hope i am not confusing
Sir, try for n=2 
@naga25french said:You are saying 2 + 2 = 4 and 4 + 4 = 8 ?If yes , yea thats again a pair ..But what i said holds good for two distinct integers
Sir, we don't want distinct integers. a and b can be same. Anyways you can get the answer now sir! 