X, Y and Z are partners In a company. In one year X receives `1/4` th part of profit, Y receives `1/5`th part of profit and Z receives Rs. 22000. How much amount (in Rs.) will X get profit?

Options

A. 10000
B. 12000
C. 15000
D. 18000

Answer

To solve the problem step by step, we will first establish the ratios of the profits received by X, Y, and Z, and then calculate how much X will receive based on the total profit.

### Step 1: Understand the profit distribution
X receives \( \frac{1}{4} \) of the total profit, Y receives \( \frac{1}{5} \) of the total profit, and Z receives Rs. 22000.

### Step 2: Set up the total profit
Let the total profit be denoted as \( TP \). We can express the shares of X and Y in terms of \( TP \):
- X's share = \( \frac{1}{4} \times TP \)
- Y's share = \( \frac{1}{5} \times TP \)

### Step 3: Find a common denominator
To combine the shares of X and Y, we need a common denominator for the fractions \( \frac{1}{4} \) and \( \frac{1}{5} \). The least common multiple of 4 and 5 is 20.

### Step 4: Express shares in terms of a common total
Now, we can express the shares of X and Y with a total profit of 20 units:
- X's share = \( \frac{1}{4} \times 20 = 5 \) units
- Y's share = \( \frac{1}{5} \times 20 = 4 \) units

### Step 5: Calculate Z's share
Since the total profit is 20 units, we can find Z's share:
- Total units = 20
- Units for X + Y = 5 + 4 = 9
- Units for Z = 20 - 9 = 11 units

### Step 6: Relate Z's share to the given amount
We know that Z receives Rs. 22000, which corresponds to 11 units. Therefore, we can find the value of 1 unit:
- Value of 1 unit = \( \frac{22000}{11} = 2000 \)

### Step 7: Calculate X's profit
Now that we know the value of 1 unit, we can calculate X's profit:
- X's share in units = 5 units
- X's profit = \( 5 \times 2000 = 10000 \)

### Final Answer
X will receive Rs. 10000 as profit.

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