Bob, Jackson, Charlie and Donald each

Question

GMATBusters’ Quant Quiz Question -1 
Bob, Jackson, Charlie and Donald each has p coins respectively. If Bob gives coins to Jackson, Charlie and Donald and finally the ratio of the numbers of coins with them is 1 : 10 : 5 : 8, what is the number of coins that Bob has given to Jackson, Charlie and Donald?
A)5p/6
B)3p/6
C)p/6
D)6p/5
E)p/5

urshi · Answer

Assume each person had 6 coins each and then bob gave away his coins so that the coins with each person became 1, 10 , 5 and 8

so , 6 coins became 1 coin. The answer choice that gives answer as 5 when we substitute p=6 is our answer option. The only answer option which satisfies this criteria is OPTION : A

Answer : OPTION A

Akriitp · Answer

Ans is A. Let us assume the exact values to be 1,10,5,8 adding all 24. everyone had equal part so 24/4 = 6 (P). but now has Bob has 1 so given 5 parts. So, answer is 5p/6

RajatJ79 · Answer

Considering Bob, Jackson, Charlie and Donald have p coins each.  Total number of coins = 4p    --- (1)

Bob gives coins to Jackson, Charlie and Donald and finally the ratio of the numbers of coins with them is 1 : 10 : 5 : 8.
 
 Total numbers of coins after the Bob gave his = 1x + 10x + 5x + 8x = 24x    --- (2)  
Taking x as the constant for mentioned ratio.

Since no new coins were introduced or removed from the coins Bob, Jackson, Charlie and Donald already had among them, the Total number of coins should remain the same i.e.
 Total (1) = Total (2) 
i.e. 4p = 24x
 i.e. p = 6x    --- (3)  
i.e. x = p/6

Which means p is a multiple of 6 and thus the number of coins Bob had before the exchange is a multiple of 6.
We can thus  rule out options D and E .

After giving coins to the others, Bob was left with 1x coins 
Let's consider option A: 5p/6

Number of coins that Bob has earlier p. number of coins Bob gave away = 5p/6 
Number of coins left with Bob = p - (5p/6) = (6p - 5p)/6 =  p/6

p/6 = x --- Considering   equation (3)

Hence, Option A is the answer.

Varunsawhney8 · Answer

Let, 
Bob(b)= P,
Jackson(J)= p,
Charlie(C)=p 
Donald(p) = p

So, total number of coins = 4p

As per the given equation, only the coins have exchanged

Ratio is given as 1:10:5:8
Let x be the common factor in the ratio

Hence,

bob= x
Jackson(J)= 10x,
Charlie(C)= 5x
Donald(p) = 8x

Submission= 24 x
We now this 24x=4p

p=6x

bob has left with x coins so he has given 5x coins

So bob has given 5p/6 coins to all three....

Mayursapkale · Answer

Let's consider initially total no of coins are 4p.
Later the a/c to ratio its 
x:10x:5x:8x total= 24x
So 4p=24x
 X=p/6

New ratio

P/6:5p/6:5p/6:4p/3

From above it is clear that Bob left with p/6 coins , that means he gave 5p/ 6 coins to others .

Posted from my mobile device

njindal · Answer

We are given following information:
Total number of coins with all four =   4p   
( This number remains constant in both scenarios since there is no external party giving more coins, instead they are exchanging among themselves)

Now moving to first scenario:
Everyone has equal number of coins, p.
Therefore, number of coins Bob has initially =  p .

Moving to next scenario:
Here, Bob gives out some of his coins to other people. 
And the final ratio of coins among them is = 1:10:5:8

Based on given ratio, we can say that Bob has 1/(1+10+5+8) of total number of coins.
=> Bob is left with  1/24 of total number of coins .

We know that total number of coins are  4p , therefore number of coins Bob is left with:
= 1/24 of 4p
=  p/6

Bob started with p coins and is left with p/6 coins.
=> Bob has given (p - p/6) coins
=> Bob has given  5p/6  coins to others.

Answer   "A"   is correct.

Archit3110 · Answer

given each has p coins ; so total coins ; 4p
target what is the number of coins that Bob has given to Jackson, Charlie and Donald? i.e x 
later Bob gives x coins so new ratio ; of Bob, Jackson, Charlie and Donald ; (p-x):(p+x/3):(p+x/3):(p+x/3)
which is same to 1 : 10 : 5 : 8
ratio of Bob coins ; 1/24 *4p = p-x
solve for x ; we get 5p/6
OPTION A

Bob, Jackson, Charlie and Donald each has p coins respectively. If Bob gives coins to Jackson, Charlie and Donald and finally the ratio of the numbers of coins with them is 1 : 10 : 5 : 8, what is the number of coins that Bob has given to Jackson, Charlie and Donald?
A)5p/6
B)3p/6
C)p/6
D)6p/5
E)p/5

ashh · Answer

Bob distributes 5p/6 coins.

Option A - 5p/6

nothing345 · Answer

Bob, Jackson, Charlie and Donald each has p coins respectively. If Bob gives coins to Jackson, Charlie and Donald and finally the ratio of the numbers of coins with them is 1 : 10 : 5 : 8, what is the number of coins that Bob has given to Jackson, Charlie and Donald?

Assume that p=6. (1+10+5+8=24 provides us with a nice number that's divisible by 4.)
Now, we know that Bob gave away 5 coins.

Substituting p=6 into the options gives us the following results:

A)5  this one matches the target value.
B)3
C)1
D)36/5
E)6/5

dishra · Answer

Bob, Jackson, Charlie and Donald each has p coins respectively. If Bob gives coins to Jackson, Charlie and Donald and finally the ratio of the numbers of coins with them is 1 : 10 : 5 : 8, what is the number of coins that Bob has given to Jackson, Charlie and Donald?
Solution: Lets assume that Bob gives x, y and z coins to Jackson, Charlie and Donald respectively.
 
Bob initially has p coins, after giving P-x-y-z coins (k)
Jackson initially has p coins, after receiving from Bob p+x, (10k)
Charlie initially has p coins, after receiving from Bob p+y, (5k)
Donald initially has p coins, after receiving from Bob p+z, ( 8k)

(p+x)/(p+y)=10k/5k=2 =>  y=x/2 - p/2

(p+x)/(p+z)=10k/8k=5/4 =>  z=4x/5 - p/5

(p+x)/(P-x-y-z)=10k/k=10 => (p+x)/(P-x-  (x/2 - p/2) -  (4x/5 - p/5) )=10 =>  x=3p/2

Total no of coins given to Jackson, Charlie and Donald= x+y+z= x+  x/2 - p/2  + 4x/5 - p/5  = 23x/10-7p/10= 23* 2p/3 *10-7p/10= 25p/30= 5p/6

bumpbot · Answer

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Bob, Jackson, Charlie and Donald each

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