JIPMAT 2022 (QA) - The population of a village is 5000. If in a year, the number of males were to increase by 5% and that of females by 3% annually, the population would grow to 5202 at the end of the year. If M is the number of males and F is the number of females in the village, then (M,F) = | PYQs + Solutions

JIPMAT 2022

Arithmetic

Percentages

Conceptual

The population of a village is 5000. If in a year, the number of males were to increase by 5% and that of females by 3% annually, the population would grow to 5202 at the end of the year. If M is the number of males and F is the number of females in the village, then (M,F) =

(3000, 2000)

(2800, 2200)

(2600, 2400)

(2700, 2300)

Correct Option: 3

Initial population =

M + F = 5000

After one year:

\newline

Males increase to =

M + 5\%M = 1.05M

\newline

Females increase to =

F + 3\%F = 1.03F

Given:

1.05M + 1.03F = 5202

...(1)

\newline

And:

M + F = 5000

...(2)

From (2):

F = 5000 - M

\newline

Substituting in (1):

\newline

1.05M + 1.03(5000 - M) = 5202

\newline

1.05M + 5150 - 1.03M = 5202

\newline

0.02M = 52

M = 2600

Therefore

F = 5000 - 2600 = 2400

The answer is

(2600, 2400)