An amount of hundred rupees in divided among two persons in the ratio `1/10 : 1/15. ` How much money does each get ?

Answer

To solve the problem of dividing 100 rupees among two persons in the ratio of \( \frac{1}{10} : \frac{1}{15} \), we can follow these steps:

### Step 1: Simplify the Ratio
The given ratio is \( \frac{1}{10} : \frac{1}{15} \). To simplify this ratio, we can cross-multiply:

\[ \frac{1}{10} : \frac{1}{15} = 1 \times 15 : 1 \times 10 = 15 : 10 \]

### Step 2: Further Simplify the Ratio
Now, we can simplify \( 15 : 10 \) by dividing both terms by 5:

\[ 15 : 10 = 3 : 2 \]

### Step 3: Set Up the Equation
Let the amounts received by the two persons be \( 3x \) and \( 2x \) respectively. According to the problem, the total amount is 100 rupees:

\[ 3x + 2x = 100 \]

### Step 4: Solve for \( x \)
Combine the terms on the left side:

\[ 5x = 100 \]

Now, divide both sides by 5 to find \( x \):

\[ x = \frac{100}{5} = 20 \]

### Step 5: Calculate the Amounts for Each Person
Now that we have \( x \), we can find the amounts for each person:

- For the first person:

\[ 3x = 3 \times 20 = 60 \text{ rupees} \]

- For the second person:

\[ 2x = 2 \times 20 = 40 \text{ rupees} \]

### Final Answer
Thus, the first person receives **60 rupees** and the second person receives **40 rupees**.

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