10 dozen apples, 15 dozen mangoes & 20 dozen oranges are kept for sale . 1/2 , `1//3^(rd) & 1//4^(th)` of each item respectively have been added . What is the total number of fruits kept for sale now ?
A. 700
B. 600
C. 580
D. 820

Options

A. D
B. A
C. B
D. C

Answer

To solve the problem, we need to calculate the total number of fruits (apples, mangoes, and oranges) after adding the specified fractions of each fruit type. Let's break it down step by step.

### Step 1: Calculate the initial number of apples
- We have 10 dozen apples.
- 1 dozen = 12 apples.
- Therefore, the total number of apples is:
\[ 10 \text{ dozen} = 10 \times 12 = 120 \text{ apples} \]

### Step 2: Add the additional apples
- We are adding \( \frac{1}{2} \) of the apples.
- The number of additional apples is:
\[ \frac{1}{2} \times 120 = 60 \text{ apples} \]
- So, the total number of apples now is:
\[ 120 + 60 = 180 \text{ apples} \]

### Step 3: Calculate the initial number of mangoes
- We have 15 dozen mangoes.
- Therefore, the total number of mangoes is:
\[ 15 \text{ dozen} = 15 \times 12 = 180 \text{ mangoes} \]

### Step 4: Add the additional mangoes
- We are adding \( \frac{1}{3} \) of the mangoes.
- The number of additional mangoes is:
\[ \frac{1}{3} \times 180 = 60 \text{ mangoes} \]
- So, the total number of mangoes now is:
\[ 180 + 60 = 240 \text{ mangoes} \]

### Step 5: Calculate the initial number of oranges
- We have 20 dozen oranges.
- Therefore, the total number of oranges is:
\[ 20 \text{ dozen} = 20 \times 12 = 240 \text{ oranges} \]

### Step 6: Add the additional oranges
- We are adding \( \frac{1}{4} \) of the oranges.
- The number of additional oranges is:
\[ \frac{1}{4} \times 240 = 60 \text{ oranges} \]
- So, the total number of oranges now is:
\[ 240 + 60 = 300 \text{ oranges} \]

### Step 7: Calculate the total number of fruits
- Now, we sum the total number of apples, mangoes, and oranges:
\[ \text{Total fruits} = 180 + 240 + 300 = 720 \]

### Final Answer
The total number of fruits kept for sale now is **720**.

---