Calculations with Percentages

A group has 60% female and 40% male members. 42% of all group members are older then 60 years, among men even 60% are older then 60. a) which percentage of the women is younger then 60? b) If a young group member (i.e. under 60 years) enters the room, what is the chance that the group member is female?

My solution would be that of the men, 24% are old, hence 18% of the group members are female and over 60 and 82% are female and younger then 60 - my solution for a) seems to be wrong though...

Let the number of male & the female member be $40x,60x$ respectively.

So, there are $100x\cdot42$%$=42x$ persons are older than $60$

Among men $40x\cdot60$%$=24x$ persons are older than $60$

So,we have $42x-24x=18x$ female persons are older than $60$

So,we have $60x-18x=42x$ female persons are younger than $60$ assuming there is no female with age exactly $60$

So, $a)$ the percentage of the women is younger than $60$ will be $\frac{42}{60}\cdot100$%$=70$%

• Among men why is it 60 times 60 and not 60 times 40? – TestGuest Mar 31 '13 at 10:14
• @TestGuest, sorry for messing up with so many $60$s. Rectified. – lab bhattacharjee Mar 31 '13 at 10:16

For these types of problems drawing the matrix is always a better methos

The matrix should look like

Less than 60             More than 60

Male x y (Total=40)

Female a b (Total=60) (Total=58) (total=42)

Given, y=24 So, b=18; and a=42

Finally we have to find percentage .So, 42/60 *100 =70%