sherlock homes and dr. watson have to travel from rajiv gandhi chowk to indira gandhi international airpot via the metro. they have enough coins of 1,5,10,25 paise. sherlock homes agrees to pay for dr. watson, only if he tells all the possible combination of coins that can be used to pay for the ticket.

Q1. how many combinations are possible, if the fare is 50 paise?

a 52 b 49 c 45 d 44

Q2. how many combination are possible, if they get in international dignitary discount of 10% i.e. the fare is 45 paise?

a 45
b 44
c 39
d 36

• 1> answer should be 49
  sol : case 1(when there is not any 25 paisa coin):
  --> when there is 5 coins of 10 paisa (10*5 +5*0 +1*0) total 1
  --> when there is 4 coins of 10 paisa (10*4 +5*2 +1*0)
  (10*4 +5*1 +1*5)
  (10*4 +5*0 +1*10) Total 3
  --> when there is 3 coins of 10 paisa (10*3 +5*4 +1*0)
  (10*3 +5*3 +1*5)
  .........so on total 5
  --> when there is 2 coins of 10 paisa (10*2 +5*6 +1*0)
  (10*3 +5*5 +1*5)
  .........so on total 7
  -->when there is 1 coin of 10 paisa (10*1 +5*8 +1*0)
  (10*3 +5*7 +1*5)
  .........so on total 9
  --> when there is 0 coin of 10 paisa (10*0 +5*10 +1*0)
  (10*0 +5*9 + 1*5)
  .........so on total 11
  So total combinations are 1+3+5+7+9+11 = 36
  
  Apply in rest 2 cases also where case 2: only one coin of 25 paisa = 12
  case 3: 2 coins of 25 paisa = 1
• 11 years agoHelpfull: Yes(33) No(5)
• Q2. 39 combinations
  
  when there is no 25 paisa coin .. 2+4+6+8+10= 30 combinations ( like two combinations with four 10 paisa coins , 4 combinations with three ten paisa coins etc.)
  when there is one 25 paisa coin .. 1+3+5= 9 combinations
• 11 years agoHelpfull: Yes(12) No(8)
• Q1.. 49 combinations are possible.
  when there is no 25 paisa coins ... 36 combinations
  when there is 1 coin of 25 paisa ......12 combinations
  when there are 2 coins of 25 paisa .. 1 combination
• 11 years agoHelpfull: Yes(9) No(10)
• 10a + 5b + 10c + 25d = 50
  0 0 0 0 2 --> 1
  0121 2
  0311 4
  0501 6
  0050 1
  0240 3
  0430 5
  0620 7
  0810 9
  0 10 0 0 11
  -----------------
  49
  
  
  10a + 5b + 10c +25d = 45
  0021 1
  0211 3
  0401 5
  0140 2
  0330 4
  0520 6
  0710 8
  0900 10
  ------------------
  39
• 8 years agoHelpfull: Yes(1) No(0)