Four Friends A, B, C and D are living in a hostel. One day As uncle came and gave him a box of laddoos, According to their rule whatever they get will be equally divided among them. So A divided the laddoos into four equal parts and he ate his part. Then B came to the room and he divided the laddoos into four equal parts and A and B ate their part. Then C came to the room he divided the laddoos into four equal parts and he ate his part. Then at the last D came to the room he also divided the laddoos into four equal parts and he ate his part. The number of laddoos D ate was 3. 1. How many laddoos did A eat?2. How many laddoos did B eat?3. How many laddoos did C eat?4. How many laddoos were there in the box altogether?

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deepa

  • Nov 27th, 2007
 

calculation is as below:

D = 3*4 = 12

C= 12*4/3 = 16

B= (16*2)/4 = 8

A= 32*4/3= 42.6

Hence A's share is 10.6+8
B ate 8 Laddoos
C ate 4

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vivekjain17

  • Dec 23rd, 2007
 

A eat 71 laddos
B eat 39 laddos
C eat 15 laddos
Total laddos were 128

Approach Since D eat 3 laddos that means when he came he saw there were 12 laddos (3*4)That means when C came in he must have seen 48 (12*4) laddos and divided then in four parts each which left 12 for D. Now important point to note here is that when C came he saw 48 laddos which were actually for C and D 24 each because if B has divided in 4 equal part he would have eat 24, give A as 24 and left 24 each for C and D. That gives us step that When B came in must have seen 96 (24*3) laddos. Which were actually for B, C and D. That gives us answer that when A got the box there should be 128 laddos which he divided in 4 equal parts of 32 each. So if we sum up laddos which A must have eat it will be (32+24+12+3)

B (24+12+3) and C (12+3) and D we know it’s 3

charenbe

  • Feb 8th, 2008
 

d=3 
3*4=12
a. b . c , d ate 3 sweet = 3

12*4=48/3=16
a, b , c ate = 16each

16*4=64/2=32
a,b=32each

32*4=128
a=128

a=128+32+16+3
a=179

b=32+16+3=51

c=16+3=19

d=3
total= 252

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satya1288

  • Mar 16th, 2008
 

Let number of laddoos be n
Now
      n = A, 3A
     
      3A = 3A/4(B), 9A/4
      
      9A/4 = 9A/16(C), 27A/16
  
      27A/16 = 27A/64(D), 81A/64

Given, D=3
       
       =>A = 64/9
     
            B = (3*64) / (9*4) = 16/3

            C = (9*64) / (16*9) = 4
  
            Total No of Laddoos = A+3A = 256/9

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vreswar

  • Mar 28th, 2008
 

Hi All,
    My approach is quite simple:

Say there are x laddoes.
A shares x/4 each to himself, B,C,D. n eates it      (A=x/4)
B comes and shares x/4*4 to each and eat    (A=x/4+x/16, B=x/16)
C comes , shares x/4*4*4 to each and eat  (A=x/4+x/16, B=x/16, c=x/64)
D comes, shares x/4*4*4*4 to each and eat (A=x/4+x/16, B=x/16, c=x/64, D=x/256)

as its given D eats 3: x/256 =3 => x=768 (Clear)

let us check it with c = x/64 => 768/64 =  12

B = x/16 =>768/16 = 48

A = x/4 + x/16 => 192+48 = 240

A=240, B=48,C=12 D=3.

rtandon

  • Jul 16th, 2008
 

1. How many laddoos did A eat?

18.66667
2. How many laddoos did B eat?
8
3. How many laddoos did C eat?
4
4. How many laddoos were there in the box altogether?
3

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rtandon

  • Jul 16th, 2008
 

1. How many laddoos did A eat?
         18.66
2. How many laddoos did B eat?
          8
3. How many laddoos did C eat?
          4
4. How many laddoos were there in the box altogether?
           42.66

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Suppose, uncle had brought x no. of ladoos.

now, they are divided in 4 parts equally:

a=x/4
b=x/4r
c=x/4
d=x/4

now, A ate his part,thus left number of ladoos are:

3x/4 which are again further divided into 4 equal parts.
thus:
 
a=3x/16
b=3x/16
c=3x/16
d=3x/16

now, a and b are people  who eat thus remaining ladoos are:

3x/4-3x/8=3x/8

i.e. remaining ladoos are: 3x/8.

now, again C came to room and divided the remaining ladoos in 4 equal parts.

thus,

a=3x/32
b=3x/32
c=3x/32
d=3x/32

now , only C eats his part thus,

remaining ladoos r: 3x/32

Finally, D comes and he divided into 4 equal parts

a=3x/128
b=3x/128
c=3x/128
d=3x/128

thus, after eating his own part the remaining ladoos r: 3x/128

which is equal to given as 3:

=> 3x/128=3
so, total number of ladoos were 128, and find the others.

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sitalakshmi

  • Mar 12th, 2009
 

It is not at all possible for D to have only 12 chocolates to divide among his four friends.
Let the number of Chocolate be X.
How Many Chocolates D had with him before he shared that with his friends?
Remember that D should have more than 1/4th of total number of chocolates before he shared with his friends.
Also the chocolates are shared only among the four friends
From A 1/4 of X, multiple of 4 (as B divide into 4 parts)
From B 1/16 of X, multiple of 4
From C 1/16 X + 1/64 X, multiple of 4 by 4
As 1/16 X is divisible by 4, 1/64 X also multiple of 4 (D divides his chocolates into four parts)


Therefore the minimum value of X is 256

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My Calculations are

Total laddoos division was = x/4+x/4+x/4+x/4
Now A eats x/4 + x/16 laddoos
B eats x/16 laddoos
C eats x/16 laddoos
D eats x/16 laddoos which is 3 as given in question

So total laddoos were 48,
A -> 15
B -> 3
C -> 3
D -> 3. Note in the question it is explicitly said in C and D's case that HE ate his part and in both the cases A and B
do not eat.

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amitraiims

  • Apr 13th, 2009
 

let there are x laddoos.
A share is x/4;
remaining is 3x/4;
now B share is 3x/16;
and A share will be x/4+3x/16;
now the remaining no. of laddoos will be 3x/8 becoz a and b ate thier part;
now C will share 3x/32;
remaining will be 3x/8-3x/32=9x/32;
and finally D share will be 9x/128;
9x/128=3
x=128/3=42.6



A ate 128/12+(3/16)*128/3=10.6+8=18.6;
B ate 3*128/3*16=8;
C ate 4
total no . of laddoos will be 42.6

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riimps

  • Jan 1st, 2010
 

I have seen the answers but could find only 1 correct answer i.e. vivekjain17's ans.

Many ppl have come to the conclusion dat there r 240 total Laddoos.. where as they missed the fact when A ate 1/4th of the total, he divided the REMAINING 3/4th laddoos into 4 parts again.

Check out this Solution:-

Let total Laddoos = x
1. A ate x/4 Laddoos, so Remaining Laddoos = 3x/4
2. Then A & B ate 1/4[3x/4] Laddoos each, so Remaining Laddoos = 1/2[3x/4] = 3x/8
3. Then A, B & C ate 1/4[3x/8] Laddoos each, so Remaining Laddoos = 1/4[3x/8] = 3x/32
4. Then A, B, C & D ate 1/4[3x/32] each and finished the Laddoos.

Date 3 Laddoos i.e. 1/4[3x/32]=3 ; x=128.
~ A ate 4 times i.e. x/4 + 1/4[3x/4] + 1/4[3x/8] + 1/4[3x/32] = 71
~ B ate 3 times i.e.          1/4[3x/4] + 1/4[3x/8] + 1/4[3x/32] = 39
~ C ate 2 times i.e.                             1/4[3x/8] + 1/4[3x/32] = 15
~ D ate 1 time  i.e.                                                 1/4[3x/32] = 3

Cross Checking (71+39+15+3 =128)

Very Simple but nt Time efficient method. I guess vivekjain17's method is time efficient but the explanation was little confusing 4 me.

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Let 'l' b number of laddoos

A divides it into 4 parts, so each wil get l/4...
now B has l/4 ladoos which he again divides into 4 parts...l/16
ate A(l/4+l/16)      B(l/16)

Now C has l/4+l/16=5l/16 ladoos...when divides into 4 equal parts 5l/64
A(l/4+l/16+5l/64)  B(l/16+5l/64)  C(5l/64)

Now D has l/4+l/16+5l/64 ladoos..when didivded into 4 equal parts 25l/256
A(l/4+l/16+5l/64+25l/256)  B(l/16+5l/64+25l/256)  C(5l/64+25l/256)  D(25l/256)

given 25l/256=3, therefore l=30.72,
C=5l/64+25l/256=5.4,
B=l/16+5l/64+25l/256=7.32
A=l/4+l/16+5l/64+25l/256=15

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diggu

  • Nov 5th, 2010
 

Let total no. of laddos be x  
                     A             B                  C             D       
   A               x/4         (                 3x/4               )

   B           ( 3x/16    3x/16 )       (          6x/16    )

   C           6x/64       6x/64         6x/64         6x/64   

   D           6x/256    6x/256       6x/256       6x/256

   now   6x/256=3 => x=128
 so A's share = x/4+3x/16+6x/64+6x/256 =71
      B's share = 3x/16+6x/64+6x/256=39
      C's share= 6x/64+6x/256=15
      D's share = 3
total laddos , x=128.

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