Vinay dropped a ball from his terrace whose height is 50 meters if the height of the ball reduces to half after every contact with the ground. What is the total distance travelled by the ball?

a. 75
b. 100
c. 150
d. 200

• s=50+2*50/2^1+2*50/2^2++2*50/2^3+....+2*50/2^infinite
  s=50[1+1+1/2^1+1/2^2+1/2^3.......]
  s=50+50[1+1/2^1+1/2^2+1/2^3.......]
  s=a/1-r ->(infinte GP)
  s=50+50[1/(1-1/2)]
  s=150
• 11 years agoHelpfull: Yes(47) No(5)
• 1) ball dropped from height of 50 mts height covered=50mts
  2)it rebounce back to height of 25 mts and falls down from 25 mts so height covered here =25+25=50mts
  3)it again rebounce to height of 12.5 mts and fall from 12.5 mts so height covered here =12.5+12.5=25
  .
  .
  50,50,25,12.5....... excluding first 50 remaining series in gp(geometric progression)to infinity with common difference=0.5 so
  sum=a/1-r
  =50/1-0.5=100
  by adding first 50 also we get total distance covered=50+100=150 meters
• 11 years agoHelpfull: Yes(35) No(0)
• infinite gp of (50, 25, 12.5,....) + 50,
  hence answe= 150
• 11 years agoHelpfull: Yes(16) No(8)
• 50+25+12.5+6.25+3.125+1.5625+0.78125+0.39+0.195+0.0976+0.0488+0.0244+0.0122+...
  =100
• 11 years agoHelpfull: Yes(16) No(24)
• series is 50+25+25+12.5+12.5+.........=50+2(25)+2(12.5).......
  sum of infinite gp is a/1-r so 50+(2*(25)/.5)=150
• 11 years agoHelpfull: Yes(9) No(1)
• Ans is 150
• 11 years agoHelpfull: Yes(6) No(7)
• when goes downward: 50+25+12.5.....
  When goes upward: 25+12.5....
  
  so total distance = downward+upward
  
  using GP sum : (50+25+12.5....)+(25+12.5....)
  = 50*(1/1-.5) + 25*(1/1-.5)
  =150
• 11 years agoHelpfull: Yes(6) No(0)
• there is one short cut for problems like these...
  formula is: area/(1-ratio)
  solution: 2*(25/(1-0.5))+50 == 150
  ratio is given 1/2
  from 50/2=25 this occurs twice because of bouncing and 50m fall occur once so i have added it.
• 11 years agoHelpfull: Yes(3) No(1)
• 150
  
  it forms two GPs as
  ((50/(1-1/2))+(25/(1-1/2)))
  
• 11 years agoHelpfull: Yes(1) No(0)
• ans is 666.625rs
  frst find CP of mixtre
  20*30+40*25=1600
  calcute 1/3 pice its 533.3rs
  calulate nw SP
  SP=125*533.3/100=666.625rs
• 11 years agoHelpfull: Yes(0) No(27)
• NO 150 will be the correct answer !!!
• 11 years agoHelpfull: Yes(0) No(0)
• (50,25,12.5,6.25........) form g.p
  ans is 150
• 9 years agoHelpfull: Yes(0) No(0)
• h(1+r/1-r) here h=50 r=1/2
• 9 years agoHelpfull: Yes(0) No(0)