Correct option is B
Solution:
Step 1: Understanding the Graph
The graph shows the price per carat of diamonds on the y-axis and the weight of a diamond in carats on the x-axis.
Observations from the graph:
A 1-carat diamond costs 2 lakh per carat.
A 2-carat diamond costs 4 lakh per carat.
The price per carat increases linearly with weight.
From this, we derive the price per carat formula:
Price per Carat = 2 × Weight (in carat).
Step 2: Determining the Maximum Possible Size
The person has 4.5 lakh to buy 4 identical diamonds.
The budget per diamond is 4.5 lakh ÷ 4 = 1.125 lakh per diamond.
Using the price formula:
Total Price of a Diamond = (Weight) × (Price per Carat).
Since Price per Carat = 2 × Weight, we set up the equation:
1.125 = Weight × (2 × Weight)
1.125 = 2 × Weight²
Weight² = 1.125/2
Weight² = 0.5625
Taking the square root:
Weight = 0.75 carat.
Step 3: Selecting the Correct Option
The largest possible diamond size is 0.75 carat, which corresponds to option (b).
