A and B started from the same point on a circular track. The ratio of their speed is n:1 (n is a whole number). If 5th and 17th time they meet at the same point, what can not be the value of n?

Options : A) 2 b) 3 c) 4 d) 6

Answer is : D

Solution :

If speed of two bodies moving in same direction in circular path are in the simplest ratio of a:b, then no. of pts they will meet = |a-b|
Let circumference of circle be 'L'.
Time for 1st meeting at any of the |a-b| pts = L/(a-b).
Time for 1st meeting at Starting Pt = LCM of (L/a, L/b).
Time for nth meeting at Starting Pt = n*LCM of (L/a, L/b).

Checking with the options :-
1 . Check Option A :
When n = 2 :
a=2,b=1.
No:of meeting pts = (2-1)=1pt.
Only meeting pt is L.
Time for first meeting = L/1.
Time for first meeting at starting pt = LCM of (L/2, L/1) = L.
Time for 5th meeting = 5L.
Time for 17th meeting = 17L.

Both tyms, they meet at pt L.
So, n=2 is valid.

Check Option B :

When n = 3 :
a=3,b=1.
No:of meeting pts = (3-1)=2pts.
Meeting pts are : L/2, L .
Time for first meeting = L/2.
Time for first meeting at starting pt = LCM of (L/3, L/1) = L.
Time for 5th meeting = 5*L/2.
Time for 17th meeting = 17*L/2.

Both tyms, they meet at pt L/2.
So, n=3 is valid.

Check Option C :

When n = 4 :
a=4,b=1.
No.of meeting pts = (4-1)=3pts.
Meeting pts are : L/3, L/2, L .
Time for first meeting = L/3.
Time for first meeting at starting pt = LCM of (L/4, L/1) = L.
Time for 5th meeting = 5*L/3.
Time for 17th meeting = 17*L/3.

Both times, they meet at pt L/3.
So, n=4 is valid.

Check Option D :

When n = 6 :
a=6, b=1.
No:of meeting pts = (6-1)=5pts.
Meeting pts are : L/5, L/4, L/3, L/2, L .
Time for first meeting = L/5.
Time for first meeting at starting pt = LCM of (L/5, L/1) = L.
Time for 5th meeting = 5*L/5 = L.
Time for 17th meeting = 17*L/5.

Both tyms, they meet at different pts namely L and L/5.

So, n=6 is not valid.

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191. A cow standing on a bridge, 5 m away from the center of the bridge.a train was coming towards the bridge from the end nearest to the cow, seeing this the cow run towards the train and manage to escape when the train was 2m away from the end of the bridge if it had run in the opposite direction it would have been hit by the train 2 m before the end of the bridge. What is the length of the bridge (in m) if speed of train is 4 times the speed of cow ??

192. Compute the number of distinct way in which 56 toffees can be distributed to 5person a,b,c,d and e so that no person receives less than 10 toffees(toffee can not be devided)??

193. How many solutions exist for (x+5)^1/3=x((x+5)^1/3)
option
a) 1 b) 2 c) 3 d) 4

194. Log a,log b,log c are in gp and m,n,o are in ap ,then (o-n)log a+(o-m)log b +(n-m)log is equal to ?
A) (o-n)log abc b) 0 c) 1

195. The method of selecting a member is to make stand all member in a straight line and are alotted roll no from right so person at right most is 1 and last is 513 if ther are 513 members so now one will start from right and will remove all alternate like 2,4 will be eliminated than when it reaches otherside will do same to right ie 512 514 will remove okk alternately so if person have to b elected where will person should stand

196. A 3 digit no in form a+4b+c is divisible by 42 then the no is neccessary divisible by a-9,b-2,c-6 d-none of these

197. How many 3 digit no sum will have sum 18
a) 51 b) 54 c) 61 d) 64

198. How many values of c in the equation x^3-5x+c result in rational roots which are integers?
a)1 b)3 c)0 d)infinite

199. What is the minimum number of distinct lines representing the altitudes,medians,and interior angles bisector of an obtuse triangle?

200.Number of numbers which have prime number of factorials in between 1 to 100 (hint no. Of prime no. = 25) ?

Page3

171. A reduction in 25% in the price of eggs will enable one to buy 4 dozen more eggs for rs 96. What is the price per dozen?

172. Ax^2+bx+c = 0 has two roots x1 and x2. If mode x1 = mode x2, then
(a) a>c (b) b>c (c) c>a (d) none

173. 1,2,1,2,2,1,2,2,2,1,2,2,2,2... Then sum of 1230 terms...?

174. 1 2 1 2 2 1 2 2 2 1 2 2 2 2 1 2 ...... Sum of the series upto 1230 terms ?

175. A dishonest dealer sells as a weight of 800gm in place of 1 kg and adds 20% impurities in sugar. What would be his profit % if he claims to be selling at cost price?

176. A borrowed rs 800@ 6% and b borrowed rs 600@ 10%.after how much time will they both have equal debts?

177. A sum of money doubles itself at compound interest in 15 yrs. In how many years it will become eight times?

178. A garden has only red,green and white flowers. 60% of the flowers have red colours,30% have green colours and 50% have white colours. If no glowers has all the three colours , what percentage of the flowers have only 1 colours?

179. 2/3=0.6666. Then find all combinations of a and b. Such that 0, 39x - 13y =1, then find out all combinations of x and y for x<1000.

180. A right triangle have sides a,b and hypotenuse h. A square inscribed in triangle having sides on a, b and touches h. Find length of side of square in terms of a ,b.?

Page4

181. From digit 0-9, how many no. Can be made such that two adjacent digits are same. Like-119,911.....

182. find the value of log22002 + log32002 + log42002 + log52002 - log102002 - log112002 - log122002 - log132002 - log142002
a) 0 b) 1 c) -1 d) 2002log2002

183. A number 'z' contains all the digits from 1 to 9 exactly once. Z is divisible by 99. What will b the number on its hundredth place.
a) 1 b) 2 c) 3 d) 4

184. puzzle of arvind and 5 ministers? How may combinations were possible and what were the other answers?

185. A(n)= 1/(log base n value 2002)
what is the value of a(2)+a(3)+a(4)+a(5)-a(10)-a(11)-a(12)-a(13)-a(14)

186. From a container having pure milk ,20% is replaced by water and the process is repeated thrice. At the end of the third operation , the milk is
a) 40% pure b) 50% pure c) 51.2% pure d) none

187. If the distance between two station is 6000 km and there are 10 stops between them train takes i^2 mints if i is odd and train takes i mints if i is even and the speed of train is 90km/hr
then how much tme it will take ?

188. Ram and shaym have a cube each. Ram paints 4 faces of cube red and rest with blue colour. Ram asked shyam to paint his cube with red and blue colour.they now started rolling it.after long observation ram found that the probability of getting same colour in both the cube is 1/3. How many faces of his cube did shyam painted red.
a) 0 b)2 c)3 d)4

189. A train 300 m log overtook a man walking along the line (in the same direction of the train) at the speed of 5km/hr and passed him in 30 sec. The train reached the station in 15 min it hass passed the man . In what time man reach the station....?

190. How many positive integers n are there such that the least common multiple of n and 1000 is 1000?

Page5

151. Milkha singh and tomar was running for a marathon....frm ramnagar to jamnagar...there are two cities between ramnagar and jamnagar ramgarh and rampur and distance between these two cities are 15 km..if milkha singh ran ramnagar to ramgarh in 90 mnts with speed 40km/hr and vkm/hr(v is whole number) speed from ramgarh to rampur in 30 mnts....as tomar is professanalist so he maintain constain speed during the marathon....and they both reached at n hour find out the value of n..
1. 5 2. 15 3. 41 4. all of above

152. Here are some student standing in circular way like 1,2,3,4,........ The 11 was standing before 40.....if there are 10 girls more than the boys find out how many boys standing against the girl....
1. 21 2. 24 3. 4.

153. If apple is coded as 118 so monkey is coded as?

154. Two trains a and b seperated by a distance of 1200m approach each other at 30m/min.a bird flying at 60 m/min flies from train a to b, returns to a flies back to b and so on till the trains meet.
a. What is the total distance travelled by the bird?
b. How many trips between the train does the bird make in all?

155. What is the difference between first "highest ever decreasing" number and second.where highest ever decreasing number are like 987,75321,954 etc?
a) 1 b) 99 c)9 d) cant be determined

156. A lump of two metals weighing 18 gm is worth rs 74 but if their weights be interchanged it would be worth rs 60.10p. If the price of one metal be rs 7.20 per gram, find the weight of the other metal in the mixture?

157. There are two vessels one containing 12 litres of water, other 6 litres of wine. If a litre be taken out of each and poured into the other, and if this be repeated four times, find how much wine will be in contained one?

158. How many values of c in the equation
x^2-5x+c=0, results in rational roots which are integer?
A) 1 B) 3 C) 0 D) infinite

159. Find the no. Of ways u can fill 3*3 grid (with 4 corners a,b,c,d) if u have 3 white marbles and 6 black marbles?

160. Two regular polygons have the number of their sides in the ratio 2:1 and their interior angle in the ratio 5:4. The number of sides of the two polygons are?

Page6

161. Square a is formed with the diagonal of square b as its sides and square b has the diagonal of square c as its side? Find the ratio of the area of square c to square a?

162. The wages of labourers in a factory increases in the ratio 22:25 and there was a reduction in the number of labourers in the ratio 15:11. Find the original wage bill if the present bill is rs 5000?

163. Assume that the distance that a car runs on 1 litre of petrol varies inversely as the square of the speed at which it is given. It gives a run of 25 km per litre at a speed of 36 km ph.at wat speed should it be driven to get a run of 36 km per litre?

164. A covers a circular track in 15 mins while b does so in 25mins. In how much time will a and b together again? They start running in the same direction from the same point?

165. 'P' is a 3 digit number. First digit from the left is a square of the last digit. None of the digit is repeated in 'p'. How many number of primesubdents are possible. (primesubdent is a number that can not be divided by 2,3,5)
a)6 b) c) d)72

166. A can contains a mixture of two liquids a and b in proportion 7:5. When 9 litres of mixture was drawn off and the can was filled with b, the proportion of a and b becomes 1:2. How many litres of mixture was contained by the can initially?

167. Y=(x^4)+4
where x is a 4 digit number. What is the probability that y is divided by 5
a)1/5 b)2/5 c)4/5 d)1

168. A dealer sells an article at a profit of 1/4 of the cost. Had he sold at a profit of 1/4 of the selling price, he would have gained rs 50 more. The cost of the article is ?

169. A grain merchant purchased 2 varieties of rice, the price of the first kind being twice that of the second. He sells the mixture for rs 28 per kg making a profit of 25%. If the ratio of the first to the second is 2:3 in the mixture, then the variety coated is?

170. I have done 4 out of 6 right in quant and 3 out of 4 in reasoning,11-12 out of 14 in verbal.how much percentile could i score

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131. A and b worked on a job for 4 hrs and finished half of it. A worked thrice as fast as b did. If b then left a and was joined by c and they finished the job in 1 hour , how long it would have taken for c to do the whole job alone?

132. Pipes a and b can fill a cistern in 20 min and 30 min and c can empty it in 15 min. If the three are kept open successively for 1 min each in the order how soon will the cistern be filled?

133. A and b can fill a cistern in 15/2 min and 5 min and c can carry of 14 litres per minute. If all pipes are open when it is full , it is emptied in 1 hours. How many litres can it hold?

134. In what time would a cistern be filled by three pipes whose diameter are 1 cm , 4/3cm, 2 cm running together.. When the largest alone will fill it in 61 minutes; the amount of water flowing in by each pipe being proportional to the square of its diameter?

135. Three men can do as much work as 5 boys and the wages of 3 boys are equal to those of 2 men. A work on which 40 boys and 15 men are employed takes 8 weeks and costs rs 15750. How long would it take if 20 boys and 20 men were employed , and how much would it costs?

136. A,B and C can do a piece of work in 12,18, and 24 days respectively. They work at it together . A stops the work after 4 days and B is called off 2 days before the work is done.in what time was the work finished?

137. If a can do as much work in 4 hours as b can do in 6 hours, or as c can do in 8 hours how long will it take c to complete a piece of work , one third of which has been done by a working 8 hours and b working 18 hours?

138. If a can do as much work in 4 hours as b can do in 8 hours, how long will it take c to complete a piece of work , one third of which has been done by a working 8 hours and b working 18 hours?

139. C does half as much in a day as a and b can do together, and b does half as much again as a. If all there working together can mow 20 hectares of barely in 16 days, how long would each , working by himself take to mow 5 hectares?

140. If 15 men or 24 women or 36 boys can do a piece of work in 12 days working 8 hours a day , how many men must be associated with 12 women and 6 boys to do another piece of work 9/4 times as great in 30 days working 6 hrs/ day?