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.3
B.3.5
C.4
D.4.5
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

• 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
  
  
  
• 9 years agoHelpfull: Yes(4) No(0)
• time taken without stoppage = > t=d/s
  so,t= 300 /60
  so time taken without stoppage is 5h.
  
  time taken with stoppage=> 300/40 =7.5h
  so difference of time due to stoppage = 7.5-5 =2.5 hrs
• 9 years agoHelpfull: Yes(4) No(0)
• 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
• 9 years agoHelpfull: Yes(3) No(0)
• 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
  
  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
  
  ANS3 1
  A
  =10 and
  1
  B
  +
  1
  C
  =
  1
  4
  (Given)
  1
  A
  +
  1
  B
  +
  1
  C
  =
  1
  4
  +
  1
  10
  =
  7
  20
  
  In 20 hours, working together they will complete 7 products.
  Thus in 40 hours they will complete 14 products
  
  
  
  
  
  
  
  
• 9 years agoHelpfull: Yes(2) No(0)
• 2q ans:-ua=30km/hr, ub=40km/hr, uc=60km/hr so,
  60+30*t=40*t so value of t=6 than total dist=240 where barun overtake arun so the total time taken by karanmala to overtake arun is 240/60=4hr the correct ans is c in 2q
• 9 years agoHelpfull: Yes(2) No(0)
• 1)after two hours arun complete 60 and barun 0
  continuously after 8 hours arun and barun will meet
  at same time kiranmala must baet in 8 hours but she can 60km in 4 hrs =240
  remaining time waiting before start that is 4hrs
  C(4)
  
• 9 years agoHelpfull: Yes(1) No(0)
• 300/60=5hr
  300/40=7 1/2 hr
  difference=2 1/2 hr
• 9 years agoHelpfull: Yes(1) No(0)
• 3)A=10 and 1B+1C=14 (Given)
  1A+1B+1C=14+110=720
  
  In 20 hours, working together they will complete 7 products.
  Thus in 40 hours they will complete 14 products
  
  
  
  
  
  
  
• 9 years agoHelpfull: Yes(0) No(0)
• Q3
  A+B+C=14
  A=1/10
  B=1/4
  then 1/10+1/4=2/20=14
  hence A+B+C=40
• 9 years agoHelpfull: Yes(0) No(0)
• qus1) If only one of the boxes has a green ball, it can be any of the 6 boxes. So, we have 6 possibilities.
  If two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.
  If 3 of the boxes have green balls, there are 4 possibilities: 123, 234, 345, 456.
  If 4 boxes have green balls, there are 3 possibilities: 1234, 2345, 3456.
  If 5 boxes have green balls, there are 2 possibilities: 12345, 23456.
  If all 6 boxes have green balls, there is just 1 possibility.
  
  Total number of possibilities = 6 + 5 + 4 + 3 + 2 + 1 = 21.
  
• 8 years agoHelpfull: Yes(0) No(0)
• 2) 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 =
  60
  10
  =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:
  While Kiranmala's distance travelled is:
  t=4 hours
  
  So, after 4 hrs, Kiranmala will start running
  
• 8 years agoHelpfull: Yes(0) No(0)
• 3
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  3)Solution:
  
  1
  A
  =10 and
  1
  B
  +
  1
  C
  =
  1
  4
  (Given)
  1
  A
  +
  1
  B
  +
  1
  C
  =
  1
  4
  +
  1
  10
  =
  7
  20
  
  In 20 hours, working together they will complete 7 products.
  Thus in 40 hours they will complete 14 products
  
• 8 years agoHelpfull: Yes(0) No(0)
• Solution:
  Option(C) is correct
  
  Let rr = running time of the train
  
  ss= stoppage time of the train
  
  DD= total distance travelled by train
  
  We have:
  
  Dr=60 and Dr+s=40Dr=60 and Dr+s=40
  
  ⇒r+sr=32⇒r+sr=32
  
  ⇒sr=12⇒sr=12
  
  As, D=300D=300 kms
  
  300r=60300r=60
  
  ⇒r=5⇒r=5 hrs and ss = 2.5 hr
• 8 years agoHelpfull: Yes(0) No(0)
• for question no. 2, answer is option C i.e. 4hrs
• 8 years agoHelpfull: Yes(0) No(0)