In fruits flies, long wing is dominant to vestigial wing. When heterozygous long-winged flies were crossed with vestigial-winged flies, 192 offsprings were produced. If an exact Mendelian ratio had been obtained, then the number of each phenotype would have been

Options

A. `{:("Long-winged Vestigial-winged"),(" 64 128"):}`
B. `{:("Long-winged Vestigial-winged"),(" 96 96"):}`
C. `{:("Long-winged Vestigial-winged"),(" 128 64"):}`
D. `{:("Long-winged Vestigial-winged"),(" 192 0"):}`

Explanation

To solve the problem, we need to determine the expected number of offspring with each phenotype when heterozygous long-winged fruit flies are crossed with vestigial-winged flies, based on Mendelian inheritance.

### Step-by-Step Solution:

1. **Identify the Genotypes**:
- Long-winged flies can be either homozygous dominant (WW) or heterozygous (Ww). In this case, we are dealing with heterozygous long-winged flies (Ww).
- Vestigial-winged flies are homozygous recessive (ww).

2. **Set Up the Cross**:
- We will perform a cross between a heterozygous long-winged fly (Ww) and a vestigial-winged fly (ww).
- This is a test cross, which helps to determine the genotype of the long-winged parent.

3. **Create a Punnett Square**:
- The gametes from the heterozygous long-winged fly (Ww) are W and w.
- The gametes from the vestigial-winged fly (ww) are w and w.
- The Punnett square will look like this:

```
W | w
----------------
w | Ww | ww
----------------
w | Ww | ww
```

4. **Analyze the Results**:
- From the Punnett square, we see:
- 2 squares show Ww (long-winged)
- 2 squares show ww (vestigial-winged)
- Therefore, the phenotypic ratio is 2 long-winged : 2 vestigial-winged, which simplifies to 1:1.

5. **Calculate Expected Numbers**:
- Given that there are 192 offspring in total, we can apply the 1:1 ratio.
- Half of 192 will be long-winged and half will be vestigial-winged.
- Therefore:
- Long-winged flies = 192 / 2 = 96
- Vestigial-winged flies = 192 / 2 = 96

6. **Final Answer**:
- If an exact Mendelian ratio had been obtained, then the number of each phenotype would have been:
- 96 long-winged flies and 96 vestigial-winged flies.