JAMIA 2023 — Mathematics PYQ

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Question

JAMIA 2023 — Mathematics PYQ

JAMIA | Mathematics | 2023

Every gram of wheat provides 0.1 gram of proteins and 0.25 gram of carbohydrates. The responding values of rice are 0.05 gram and 0.5 gram respectively. The minimum daily requirements of proteins & carbohydrates for an average child are 50 gram & 200 gram respectively. Then in what quantities wheat & rice be mixed in daily diet to provide minimum daily requirement of proteins & carbohydrates at minimum cost?

Choose the correct answer:

Explanation

1. Variables define karein:

Maana ki Wheat ( $x$ ) grams hai aur Rice ( $y$ ) grams hai.

2. Constraints (Shartein) banayein:

Proteins ke liye:

0.1x + 0.05y \geq 50

Multiply by 100:

10x + 5y \geq 5000 \implies 2x + y \geq 1000 \quad \dots (1)

Carbohydrates ke liye:

0.25x + 0.5y \geq 200

Multiply by 100:

25x + 50y \geq 20000 \implies x + 2y \geq 800 \quad \dots (2)

Non-negativity:

x \geq 0, y \geq 0

3. Intersection Point nikalne ke liye Equations solve karein:

Equation (2) se $x$ ki value nikalein:

x = 800 - 2y

Isse Equation (1) mein rakhein:

2(800 - 2y) + y = 1000

1600 - 4y + y = 1000

-3y = -600

y = 200

Ab $x$ ki value nikalein:

x = 800 - 2(200)

x = 400

4. Final Answer:

Wheat: $400$ grams
Rice: $200$ grams