Question

A new species lays exactly 120 eggs out of which 50\% are male and 50\% are female. The female insect hatch and grow in a span of 20 days to lay eggs by themselves. On 1st April 2018, an insect laid 120 eggs. Find how many eggs will be hatched (approx.) by the end of May 2018?

• A. 12960
• B. 1269000
• C. 12690000
• D. None of these

Hint:

For multi-generation growth problems, create a timeline and carefully track which batches have matured by the target date. Only count those as “hatched.”

Answer 1

The Correct Option is D

[-2mm] Step 1: Understanding the cycle
Each batch of eggs requires 20 days to hatch and produce new egg-laying females. Time span from 1 April to 31 May = 61 days. The 20-day checkpoints are: Day 0 (Apr 1), Day 20 (Apr 21), Day 40 (May 11), Day 60 (May 31).
Step 2: Given conditions
- Each female lays \(120\) eggs.
- 50\% of the eggs are females.
If there are \(F\) females, eggs laid = \(120F\), females in that batch = \(60F\).
Step 3: Generation-wise calculation
\underline{Day 0 (Apr 1):}
Eggs \(E_0 = 120\), Females \(F_0 = 60\).
\underline{Day 20 (Apr 21):}
Eggs \(E_1 = 120 \times 60 = 7200\), Females \(F_1 = 3600\).
\underline{Day 40 (May 11):}
Eggs \(E_2 = 120 \times 3600 = 432000\), Females \(F_2 = 216000\).
\underline{Day 60 (May 31):}
Eggs \(E_3 = 120 \times 216000 = 25920000\).
Step 4: Which eggs are hatched by 31 May?
Eggs take 20 days to hatch. Thus, by 31 May, only batches laid on or before Day 40 will have hatched: \[ \text{Total hatched} = E_0 + E_1 + E_2 = 120 + 7200 + 432000 = 439{,}320 \] Step 5: Conclusion
The value \(439{,}320\) does not match any given option, hence: \[ \boxed{\text{None of these}} \]