An Indian company, having its registered office at Gurugram, is engaged in manufacturing of consumer goods at Noida. The goods manufactured by the company are sold in Indian market and exported to Europe. Company produces five products namely ‘P’, ‘Q’, ‘R’, ‘S’ and ‘T’. Total production of the company for the financial year 2021-22 is 3,000 tonnes and the turnover of the company is ₹ 50 million. Analysis of the production and net revenue generation shows that production of product ‘P’ is 21% of the total production and 18% of the turnover is attributable to product ‘P’; production of ‘Q’ is 16% of the total production and 17% of the turnover is attributable to ‘Q’; ‘R’ accounts for 18% of the total production and 20% of the turnover; ‘S’ accounts for 20% of the total production and 25% of the turnover, and; ‘T’ accounts for 25% of total production and 20% of turnover.

Which product has the highest selling price per tonne?

Correct Answer: S

To determine which product has the highest selling price per tonne, we need to calculate the selling price per tonne for each product based on the total production volume and turnover provided.

Given Data:

Total Production = 3,000 tonnes
Total Turnover = ₹ 50 million = ₹ 50,000,000

The selling price per tonne for any product can be expressed as:

$\text{Selling Price per Tonne}=\frac{\text{Turnover of Product}}{\text{Production Volume of Product}}$

Let's calculate the turnover, production volume, and selling price per tonne for each product:

1. Product P:
Production = 21% of 3,000 tonnes = 630 tonnes
Turnover = 18% of ₹ 50,000,000 = ₹ 9,000,000
Selling Price per tonne = $\frac{\mathrm{9,000,000}}{630}\approx \text{₹}\mathrm{14,285.71}$

2. Product Q:
Production = 16% of 3,000 tonnes = 480 tonnes
Turnover = 17% of ₹ 50,000,000 = ₹ 8,500,000
Selling Price per tonne = $\frac{\mathrm{8,500,000}}{480}\approx \text{₹}\mathrm{17,708.33}$

3. Product R:
Production = 18% of 3,000 tonnes = 540 tonnes
Turnover = 20% of ₹ 50,000,000 = ₹ 10,000,000
Selling Price per tonne = $\frac{\mathrm{10,000,000}}{540}\approx \text{₹}\mathrm{18,518.52}$

4. Product S:
Production = 20% of 3,000 tonnes = 600 tonnes
Turnover = 25% of ₹ 50,000,000 = ₹ 12,500,000
Selling Price per tonne = $\frac{\mathrm{12,500,000}}{600}\approx \text{₹}\mathrm{20,833.33}$

5. Product T:
Production = 25% of 3,000 tonnes = 750 tonnes
Turnover = 20% of ₹ 50,000,000 = ₹ 10,000,000
Selling Price per tonne = $\frac{\mathrm{10,000,000}}{750}=\text{₹}\mathrm{13,333.33}$

Alternative Quick Comparison Method:
Since total turnover and total production are constant for all products, the selling price per tonne is directly proportional to the ratio of percentage of turnover to percentage of production:

$\text{Ratio}=\frac{\text{\% Turnover}}{\text{\% Production}}$

• For P: $\frac{18}{21}\approx 0.857$
• For Q: $\frac{17}{16}=1.0625$
• For R: $\frac{20}{18}\approx 1.111$
• For S: $\frac{25}{20}=1.250$
• For T: $\frac{20}{25}=0.800$

Product S has the highest ratio of 1.25, indicating that it generates the maximum revenue per unit of production mass. Therefore, Product S has the highest selling price per tonne.