The populations of villages X and Z are 16,000 and 12,800 respectively. The ratio of the population of village X to village Y is 4 : 5. Three manufacturers A, B, and C produce cycles for these three villages. The cycles manufactured by A, B, and C are in the ratio 22 : 19 : 20, assuming each person buys one cycle. Of the cycles produced, 60%, 75%, and 80% by A, B, and C respectively are sold. Each cycle sells for Rs. 8,000.

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1756744090/aptidude_questions/fvnwmd3ujez5f2qzypqx.png)

Using the above information, answer the following:

What is the revenue generated from village Y if every person in villages X and Z purchases a cycle?

Question

The populations of villages X and Z are 16,000 and 12,800 respectively. The ratio of the population of village X to village Y is 4 : 5. Three manufacturers A, B, and C produce cycles for these three villages. The cycles manufactured by A, B, and C are in the ratio 22 : 19 : 20, assuming each person buys one cycle. Of the cycles produced, 60%, 75%, and 80% by A, B, and C respectively are sold. Each cycle sells for Rs. 8,000.

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1756744090/aptidude_questions/fvnwmd3ujez5f2qzypqx.png)

Using the above information, answer the following:

What is the revenue generated from village Y if every person in villages X and Z purchases a cycle?

Accepted Answer

**Solution:**

1. Calculate the population of village Y using the ratio of X to Y:
   - Given ratio X : Y = 4 : 5
   - Population of X = 16,000
   - So, population of Y = $ \frac{5}{4} \times 16,000 = 20,000 $

2. Total population across the three villages:
   - X + Y + Z = 16,000 + 20,000 + 12,800 = 48,800

3. Cycles manufactured by A, B, and C are in the ratio 22 : 19 : 20, total parts = 22 + 19 + 20 = 61.

4. Calculate cycles produced by each manufacturer:
   - A: $ \frac{22}{61} \times 48,800 = 17,600 $
   - B: $ \frac{19}{61} \times 48,800 = 15,200 $
   - C: $ \frac{20}{61} \times 48,800 = 16,000 $

5. Cycles supplied (sold) by each manufacturer:
   - A: 60% of 17,600 = 0.60 \times 17,600 = 10,560
   - B: 75% of 15,200 = 0.75 \times 15,200 = 11,400
   - C: 80% of 16,000 = 0.80 \times 16,000 = 12,800

6. Total cycles supplied = 10,560 + 11,400 + 12,800 = 34,760

7. Cycles purchased by villages X and Z = 16,000 + 12,800 = 28,800

8. Cycles supplied to village Y = Total cycles supplied - cycles purchased by X and Z
   - = 34,760 - 28,800 = 5,960

9. Revenue from village Y = Number of cycles supplied to Y \times Selling price per cycle
   - = 5,960 \times 8,000 = Rs. 47,680,000 = Rs. 4.768 crore

**Answer:** Rs. 4.768 crore

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