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1. There are 6 boxes numbered 1,2,...6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is:
A.5
B.21
C.33
D.60
E.27
2. Arun, Barun and Kiranmala start from the same place and travel in the same direction at speeds of 30, 40 and 60 km per hour respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start?
A. 3hr
B. 3.5hr
C. 4hr
D. 4.5hr
E. None of these
3. A work is done by three person A,B and C. A alone takes 10 hours to complete a single product but B and C working together takes 4 hours, for the completion of the same product. If all of them worked together and completed 14 products, then how many hours have they worked?
A.20 hrs
B.28 hrs
C.40 hrs
D.54 hrs
E.none of these
4. A bus without stopping travels at an average speed of 60 km/hr and with stoppages at an average speed of 40 km/hr. What is the total time taken by the bus for stoppages on a route of length 300km?
A.4 hr
B.3 hr
C.2.5 hr
D.3.5 hr
E.None of above
5. 1/3 of a certain journey is covered at the rate of 25km/hr,1/4 at the rate of 30 km/hr and the rest is 50 km/hr.the avg speed for the whole journey is :
A.30km/hr
B.30km/hr
C.33 1/3 km/hr
D. 37 1/12 km/hr
E. None of these.
6. A student has got marks in five subjects in the ratio 2:3:4:5:6 .The maximum marks of subjects in same sequence are in ratio 6:5:8:4:7.Total percentage of marks scored by him is 48%. Find the maximum percentage obtained by him in a subject?
A. 65
B. 78
C. 96
D. 90
E. None of these
7. Find out the ratio of milk to that of water ,if a mixture is formed after mixing milk and water of 3 different vessels containing the mixture of milk to that of water in the proportion 3:2, 7:3, 9:2 respectively.
A. 235:98
B. 97:233
C. 233:97
D. 233:98
E. None of these
8. A bus covers a certain distance at a speed of 54 km/h excluding stoppages and 45 km/h including stoppages. For how many minutes does the bus stop per hour?
A. 20min.
B. 5min.
C. 7min.
D. 10min.
E. None of these
9. 72 L of a mixture of milk and water contains 18% of water. How much water must be added to make the water 28% in the mixture?
A. 10 L
B. 5 L
C. 15 L
D. 12.5 L
E. None of these
10. A Lieutenant wishes to draw up his 1688 soldiers in the form of a solid square. After arranging them, he found that some of them are left over. How many are left?
A. 6
B. 5
C. 8
D. 9
E. None of these
ANSWERS & EXPLANATION:
Explanation-1: If only one of the boxes has a green ball, it can be any of the 6 boxes. So, this can be achieved in 6 ways.
If two of the boxes have green balls and then there are 5 arrangement possible. i.e., the two boxes can one of 1-2 or 2-3 or 3-4 or 4-5 or 5-6.
If 3 of the boxes have green balls, there will be 4 options in which the 3 boxes are in consecutive positions. i.e., 1−2−3 or 2−3−4 or 3−4−5 or 4−5−6
If 4 boxes have green balls, there will be 3 options. i.e., 1−2−3−4 or 2−3−4−5 or 3−4−5−6
If 5 boxes have green balls, then there will be 2 options. i.e., 1−2−3−4−5 or 2−3−4−5−6
If all 6 boxes have green balls, then there will be just 1 options.
Total number of options =6+5+4+3+2+1= 21
Explanation-2: ANS 2-Option(C) is correct
Let us assume that Arun started running at 10 AM and Barun started at 12 noon.
So, in these two hours distance travelled by Arun is 60 km and the relative speed of Barun w.r.t Arun is 10 km/hr.
So Barun will overtake Arun after =6010=6 hrs
So, Barun reaches there at 6 PM.
So, Kiranmala also overtakes Arun at 6 PM.
Let us assume Kiranmala takes t time to overtake Arun and the relative speed of Kiranmala w.r.t Arun is 30 km/hr and Arun ran for 8 hrs.
So, distance travelled by Arun is:=time×speed=8×30 -------- (1)
While Kiranmala's distance travelled is:=t×60 -------- (2)
Since distance traveled by them is equal,
⇒(1)=(2)
⇒8×30=t×60
t=4 hours
So, after 4 hrs, Kiranmala will start running
Explanation-3: 1/A=10 and 1/B+1/C=14 (Given)
1/A+1/B+1/C=1/14+1/10=7/20
In 20 hours, working together they will complete 7 products.
Thus in 40 hours they will complete 14 products
OR A+B+C=14
A=1/10
B=1/4
then 1/10+1/4=2/20=14
hence A+B+C=40
Explanation-4: Let r = running time of the train
s= stoppage time of the train
D= total distance travelled by train
We have:
Dr=60 and D(r+s)=40
⇒ (r+s)r=32
⇒ sr=½
As, D=300 kms
300r=60
⇒ r=5 hrs and s= 2.5 hr
Explanation-5: let assume total distance will be 120km then
distance traveled at teh speed 25km/hr=1/3*120=40km the time=40/25=1.6hrs
distance traveled at the speed 30km/hr=1/4*120=30kmthe time is=30/30=1 hr
then remaining distance is 120-40-30=50km
the time taken to travel 50km=50/50=1hr
so total time is=1.6+1+1=3.6 hrs
so avg speed =120/3.6=33.33km/hr
OR
Let total distance be x.
T=x/3*25+x/4*30+5x/12*50=x/75+x/120+x/120.
Therefore avg.speed=x/9x/300=100/3=33 1/3.Ans.
Explanation-6: lets marks obtain 2x,3x,4x,5x,6x.
total marks 6y,5y,8y,4y,7y.
addition of marks obtain=(2x+3x+4x+5x+6x)=20x
addition of total marks=(6y+5y+8y+4y+7y)=30y
so percentage=(20x/30y)*100
(20x/30y)*100=48
so,x/y=18/25
as we observed 5x/4y is the maximum marks
so 5x/4y=5/4*18/25*100=90%
Explanation-7: we have 3:2 i.e 3+2=5, 7:3 i.e 7+3=10, 9:2 i.e 9+2 =11
Take the LCM of 5,10,11 = 110
for vessel 1
Milk (110/5)*3=66
Water(110/5)*2=44
Likewise,
for vessel 2
milk= 77 water =33
for vessel 3
milk =90 water=20
add up milk nd Water differently i.e. 233:97Ans.
Explanation-8: Due to stoppages,it covers (54-45) 9 km less.
time taken by bus stop per hour=9/54*60=10 min
Explanation-9: Let the required quantity of added water is m L.
Now, 72 * 82 / {100 / (72*82/100)} + m = (72*18 + 100m) / (72*82) = 28/72
=> 1296 + 100m = 2296
=> 100m = 1000 => m = 10 L.
Explanation-10: Correct answer is 7 as (41^1 + 7 = 1688)
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