A certain number of candies is distributed equally among Alice, Ben, C

Question

A certain number of candies is distributed equally among Alice, Ben, Cane and Dino. Alice further distributes $$\frac{3}{4}$$ of his candies equally among the other three people. Later, Ben gives half of his candies to Dino. What fraction of the total number of candies does Dino have in the end?

(A) $$\frac{15}{8}$$

(B) $$\frac{5}{16}$$

(C) $$\frac{7}{16}$$

(D) $$\frac{15}{32}$$

(E) $$\frac{17}{32}$$

(A)  \frac{15}{8}

(B)  \frac{5}{16}

(C)  \frac{7}{16}

(D)  \frac{15}{32}

(E)  \frac{17}{32}

Chibvike · Answer

Let's assume they all have 1 candle each; A+B+C+D=4

Alice further distributes $3/4; (3/4)/3 = 1/4

At this point the other three persons (that is, Ben, Cane and Dino) have 5/4 each

Ben who currently has 5/4 gives half of his candies to Dino who also has 5/4

Dino's total balance becomes his (5/4) + half of Ben's 5/4 which is (1/2)*(5/4) = 5/8

Dino; (5/4) + 5/8 = 15/8

Recall we have a total of 4 candles

Dino's balance as a fraction of the total is (15/8)/4 = 15/32

Answer choice D

Krunaal · Answer

Since we can see 2 fractions in the question viz. 3/4 and 1/2; let's assume each have 8 candies (8 because after doing its 3/4th, it could still be halved and will still give an integer)

So, A => 8, B => 8, C => 8, D => 8, Total candies => 32

Alice distributes 3/4th of his candies i.e. 6 of his candies equally among other 3, i.e. B, C, D each get 2 candies

Now, A => 2, B => 10, C => 10, D => 10

B gives half of his candies i.e. 5 of his candies to D

Now, A => 2, B => 5, C => 10, D => 15

Fraction of total candies D has = 15/32

Answer D.

Carcass · Answer

Let's denote the total number of candies as $T$.
There are 4 people: Alice (A), Ben (B), Cane (C), and Dino (D).

Step 1: Initial Distribution
The candies are distributed equally among the four people.
- Alice: $ A_0=\frac{T}{4} $

- Ben: $ B_0=\frac{T}{4} $

- Cane: $ C_0=\frac{T}{4} $

- Dino: $ D_0=\frac{T}{4} $

Step 2: Alice Distributes Her Candies

Alice distributes $ \frac{3}{4} $ of her candies equally among the other three people (Ben, Cane, and Dino).

The amount Alice distributes is $ \frac{3}{4} 	imes A_0=\frac{3}{4} 	imes \frac{T}{4}=\frac{3 T}{16} $.

This amount is divided equally among 3 people, so each receives: $ \frac{3 T}{16} \div 3=\frac{T}{16} $.

Let's update their candy counts:

- Alice's remaining candies: $ A_1=A_0-\frac{3}{4} A_0=\frac{1}{4} A_0=\frac{1}{4} 	imes \frac{T}{4}=\frac{T}{16} $

- Ben's candies: $ B_1=B_0+\frac{T}{16}=\frac{T}{4}+\frac{T}{16}=\frac{4 T}{16}+\frac{T}{16}=\frac{5 T}{16} $

- Cane's candies: $ C_1=C_0+\frac{T}{16}=\frac{T}{4}+\frac{T}{16}=\frac{4 T}{16}+\frac{T}{16}=\frac{5 T}{16} $

- Dino's candies: $ D_1=D_0+\frac{T}{16}=\frac{T}{4}+\frac{T}{16}=\frac{4 T}{16}+\frac{T}{16}=\frac{5 T}{16} $

Step 3: Ben Gives Candies to Dino

Ben gives half of his current candies to Dino.

The amount Ben gives to Dino is $ \frac{1}{2} 	imes B_1=\frac{1}{2} 	imes \frac{5 T}{16}=\frac{5 T}{32} $.

Let's update their final candy counts:

- Alice's final candies: $ A_2=\frac{T}{16} $

- Ben's final candies: $ B_2=B_1-\frac{5 T}{32}=\frac{5 T}{16}-\frac{5 T}{32}=\frac{10 T}{32}-\frac{5 T}{32}=\frac{5 T}{32} $

- Cane's final candies: $ C_2=\frac{5 T}{16} $

- Dino's final candies: $ D_2=D_1+\frac{5 T}{32}=\frac{5 T}{16}+\frac{5 T}{32}=\frac{10 T}{32}+\frac{5 T}{32}=\frac{15 T}{32} $

Final Question:
What fraction of the total number of candies does Dino have in the end?

Dino has $ \frac{15 T}{32} $ candies. The total number of candies is $T$.

The fraction is $ \frac{15 T / 32}{T}=\frac{15}{32} $.

The final answer is $ \frac{15}{32} $.

A certain number of candies is distributed equally among Alice, Ben, C

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A certain number of candies is distributed equally among Alice, Ben, C

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