A profit of Rs. 960 is divided between 'A' and B in the ratio `1/3:1/5`. The difference of their profits is:

Options

A. Rs 120
B. Rs 160
C. Rs 180
D. Rs 240

Answer

To solve the problem of dividing a profit of Rs. 960 between A and B in the ratio of \( \frac{1}{3} : \frac{1}{5} \) and finding the difference in their profits, we can follow these steps:

### Step 1: Simplify the Ratio
The given ratio is \( \frac{1}{3} : \frac{1}{5} \). To simplify this, we can find a common denominator. The least common multiple of 3 and 5 is 15.

- To convert \( \frac{1}{3} \) to a fraction with a denominator of 15, we multiply both the numerator and denominator by 5:
\[ \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15} \]

- To convert \( \frac{1}{5} \) to a fraction with a denominator of 15, we multiply both the numerator and denominator by 3:
\[ \frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15} \]

Thus, the simplified ratio of A to B is \( 5 : 3 \).

### Step 2: Calculate the Total Parts
The total parts in the ratio \( 5 : 3 \) is:
\[ 5 + 3 = 8 \text{ parts} \]

### Step 3: Calculate the Value of Each Part
The total profit is Rs. 960. To find the value of one part, we divide the total profit by the total parts:
\[ \text{Value of one part} = \frac{960}{8} = 120 \text{ Rs.} \]

### Step 4: Calculate Individual Profits
Now we can calculate the individual profits for A and B:
- Profit of A (5 parts):
\[ \text{Profit of A} = 5 \times 120 = 600 \text{ Rs.} \]

- Profit of B (3 parts):
\[ \text{Profit of B} = 3 \times 120 = 360 \text{ Rs.} \]

### Step 5: Calculate the Difference in Profits
Finally, we find the difference between the profits of A and B:
\[ \text{Difference} = 600 - 360 = 240 \text{ Rs.} \]

### Final Answer
The difference in their profits is Rs. 240.

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