Present population of town is 40000 having males and females. If the…
2023
Present population of town is 40000 having males and females. If the population of males is increased by 8% and the population of females is increased by 6%, then after 1 year population becomes 4280. Find the number of females ?
- A.
22000
- B.
24000
- C.
18000
- D.
20000
Attempted by 22 students.
Show answer & explanation
Correct answer: D
Solution:
Let F be the number of females and M be the number of males. Then M + F = 40,000.
After one year, males increase by 8% and females by 6%, so the total becomes 1.08·M + 1.06·F = 42,800. (The problem statement's 4280 appears to be a missing zero; we proceed with 42,800 to match the context and options.)
Substitute M = 40,000 − F into the equation: 1.08(40,000 − F) + 1.06F = 42,800.
Expand and simplify: 43,200 − 1.08F + 1.06F = 42,800 ⇒ 43,200 − 0.02F = 42,800.
Rearrange: −0.02F = −400 ⇒ F = 400 / 0.02 = 20,000.
Answer: 20,000 females.