In a plant, two genes have cumulative influence on the weight of fruits. Each dominant allele adds 10g to a minimum basic weight of 30g. In a cross between dihybrid plants having fruits weighing 50g each, what percentage of the offspring would have fruits weighing 40g :-

Options

A. `12.5%`
B. 0.25
C. `37.5%`
D. 0.5

Answer

To solve the problem, we need to analyze the genetic cross between dihybrid plants that influence the weight of fruits. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Genetic Basis
In this scenario, we have two genes (let's call them A and B) that influence the weight of the fruits. Each dominant allele (A or B) adds 10g to a minimum basic weight of 30g.

### Step 2: Determine the Weight Contribution
- The minimum weight of the fruit is 30g (when both alleles are recessive: aa and bb).
- Each dominant allele contributes an additional 10g.
- Therefore, the weights can be calculated as follows:
- Genotype **AA BB**: 30g + 20g = 50g
- Genotype **AA Bb**: 30g + 10g + 10g = 50g
- Genotype **Aa BB**: 30g + 10g + 10g = 50g
- Genotype **Aa Bb**: 30g + 10g + 10g = 50g
- Genotype **AA bb**: 30g + 10g = 40g
- Genotype **Aa bb**: 30g + 10g = 40g
- Genotype **aa BB**: 30g + 20g = 50g
- Genotype **aa Bb**: 30g + 10g = 40g
- Genotype **aa bb**: 30g = 30g

### Step 3: Set Up the Dihybrid Cross
Since we are dealing with dihybrid plants, we can set up a Punnett square for the cross between two dihybrid plants (AaBb x AaBb). The gametes produced will be:
- AB, Ab, aB, ab (from one parent)
- AB, Ab, aB, ab (from the other parent)

### Step 4: Fill in the Punnett Square
The Punnett square will have 16 squares (4x4) and we can fill in the combinations:
- **AA BB**: 50g
- **AA Bb**: 50g
- **Aa BB**: 50g
- **Aa Bb**: 50g
- **AA bb**: 40g
- **Aa bb**: 40g
- **aa BB**: 50g
- **aa Bb**: 40g
- **aa bb**: 30g

### Step 5: Count the Offspring with 40g
From the filled Punnett square, we find the genotypes that yield a weight of 40g:
- **AA bb**: 40g
- **Aa bb**: 40g
- **aa Bb**: 40g

There are 4 combinations that result in a weight of 40g.

### Step 6: Calculate the Percentage
To find the percentage of offspring that will have fruits weighing 40g:
- Total combinations = 16
- Combinations resulting in 40g = 4

Percentage = (Number of 40g fruits / Total combinations) * 100
= (4 / 16) * 100 = 25%

### Final Answer
The percentage of the offspring that would have fruits weighing 40g is **25%**, which corresponds to **0.25**.

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