The ratio between the number of males and females in a college is 21:22. If the number of males are increased by 20%

The ratio between the number of males and females in a college is 21:22. If the number of males are increased by 20% and the number of female increased by 30%. What is new ratio of males and females in the college?

a) 127:143
b) 125:143
c) 128:143
d) 126:143

Ans : d) 126:143

UP Police SI Exam Paper : Mathematics

Solution

Let the initial number of males be ( 21x ) and the initial number of females be ( 22x ), where ( x ) is a common multiplier.

Step 1: Calculate the increased number of males.

The number of males is increased by 20%, so the new number of males becomes:
New number of males = $21x + 20\% \text{ of } 21x = 21x + \frac{20}{100} \times 21x = 21x + 4.2x = 25.2x$

Step 2: Calculate the increased number of females.

The number of females is increased by 30%, so the new number of females becomes:
New number of females = $22x + 30\% \text{ of } 22x = 22x + \frac{30}{100} \times 22x = 22x + 6.6x = 28.6x$

Step 3: Calculate the new ratio.

The new ratio of males to females is:
New ratio = $\frac{25.2x}{28.6x} = \frac{25.2}{28.6}$

New ratio = $\frac{252}{286} = \frac{126}{143}$
Thus, the new ratio of males to females is ( 126:143 ).