population of two small cities A and C are 16,000 and 12,800 respectively . Ratio of population of city A to that of B is 4:5. Three manufactures, X,Y and Z supply cycles in these three cities. These manufactured cyceles in the ratio of `22:19:20(X:Y:Z)` by assuming that each person will buy one cycle and `60% 75^ and 80%` of the cycle manufactured by X,Y and Z. respectively are sold and selling price of each cycle is Rs. 8,000.
(a) `"Supply"=("Revenu")/("Selling price of a cycle")`
(b) `"Demand %"=("Number of cycles ordered by customers")/("Total number of cycles remainded with manufacturer")`
What is th e profit earned by manufacturer Z from city A, if total revenue earhed by all three manufacturers in city A is `9.6` crore and number oc cycles supplid by all of them are equal and cost price of each cycle is 6000 ?

Options

A. 90 lakh
B. 50 lakh
C. 75 lakh
D. 80 lakh

Explanation

To solve the problem step by step, let's break down the information given and calculate the profit earned by manufacturer Z from city A.

### Step 1: Determine the Population of City B
Given the ratio of the population of city A to city B is 4:5, we can find the population of city B.

Let the population of city B be \( P_B \).

Using the ratio:
\[ \frac{P_A}{P_B} = \frac{4}{5} \]
Substituting the known value of \( P_A = 16,000 \):
\[ \frac{16,000}{P_B} = \frac{4}{5} \]
Cross-multiplying gives:
\[ 4P_B = 16,000 \times 5 \]
\[ 4P_B = 80,000 \]
\[ P_B = \frac{80,000}{4} = 20,000 \]

### Step 2: Determine the Total Population of Cities A, B, and C
The populations are:
- City A: 16,000
- City B: 20,000
- City C: 12,800

Total population:
\[ P_{total} = P_A + P_B + P_C = 16,000 + 20,000 + 12,800 = 48,800 \]

### Step 3: Calculate the Number of Cycles Manufactured by Each Manufacturer
The ratio of cycles manufactured by X, Y, and Z is 22:19:20. Let the total number of cycles manufactured be \( C \).

Let the number of cycles manufactured by:
- X = \( 22x \)
- Y = \( 19x \)
- Z = \( 20x \)

Total cycles manufactured:
\[ 22x + 19x + 20x = 61x \]

### Step 4: Calculate the Number of Cycles Sold by Each Manufacturer
According to the problem:
- 60% of cycles manufactured by X are sold.
- 75% of cycles manufactured by Y are sold.
- 80% of cycles manufactured by Z are sold.

Thus, the cycles sold:
- Sold by X = \( 0.6 \times 22x = 13.2x \)
- Sold by Y = \( 0.75 \times 19x = 14.25x \)
- Sold by Z = \( 0.8 \times 20x = 16x \)

### Step 5: Calculate the Total Revenue from City A
The total revenue earned by all manufacturers in city A is given as Rs. 9.6 crore, which is Rs. 96,00,000.

### Step 6: Determine the Number of Cycles Supplied by Each Manufacturer
Since the number of cycles supplied by all manufacturers is equal, let’s denote the number of cycles supplied by each manufacturer as \( S \).

From the total revenue:
\[ \text{Total Revenue} = \text{Number of cycles sold} \times \text{Selling price per cycle} \]
Selling price per cycle = Rs. 8,000.

Thus, the total cycles sold by all manufacturers in city A:
\[ S \times 8000 = 96,00,000 \]
\[ S = \frac{96,00,000}{8000} = 1200 \]

### Step 7: Calculate the Profit Earned by Manufacturer Z
Cost price of each cycle = Rs. 6,000.

Profit per cycle = Selling price - Cost price:
\[ \text{Profit} = 8000 - 6000 = 2000 \]

Since all manufacturers sold equal cycles, the profit earned by manufacturer Z from city A:
\[ \text{Profit by Z} = \text{Profit per cycle} \times \text{Number of cycles sold by Z} \]
\[ \text{Profit by Z} = 2000 \times 400 = 800,000 \]

### Final Answer
The profit earned by manufacturer Z from city A is Rs. 8,00,000.