A man has given one-fourth part of his property to his daughter, half part to his sons and one-fifth part given as charity. How much part of his property he has given?

Options

A. `1/20`
B. `19/20`
C. `1/10`
D. `9/10`

Answer

To solve the problem step by step, we need to find out how much of the man's property he has given away in total. Let's break it down:

### Step 1: Identify the fractions given to each recipient
- The man gives:
- One-fourth (1/4) of his property to his daughter.
- Half (1/2) of his property to his sons.
- One-fifth (1/5) of his property to charity.

### Step 2: Find a common denominator
To add these fractions together, we need to find a common denominator. The denominators we have are 4, 2, and 5.

- The least common multiple (LCM) of 4, 2, and 5 is 20.

### Step 3: Convert each fraction to have the common denominator
Now we convert each fraction to have the denominator of 20:
- For 1/4:
\[ \frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20} \]
- For 1/2:
\[ \frac{1}{2} = \frac{1 \times 10}{2 \times 10} = \frac{10}{20} \]
- For 1/5:
\[ \frac{1}{5} = \frac{1 \times 4}{5 \times 4} = \frac{4}{20} \]

### Step 4: Add the fractions
Now we can add all the fractions together:
\[ \frac{5}{20} + \frac{10}{20} + \frac{4}{20} = \frac{5 + 10 + 4}{20} = \frac{19}{20} \]

### Step 5: Conclusion
The total part of the property that the man has given away is:
\[ \frac{19}{20} \]

Thus, the man has given away \( \frac{19}{20} \) of his property.

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