If 70% of the women in a room are over 50 years old and 80% of the peo

Question

If 70% of the women in a room are over 50 years old and 80% of the people in the room are women, what is the ratio of the number of women 50 years old or less to the number men in the room?

A. 3 : 7
B. 4 : 1
C. 6 : 5
D. 7 : 10
E. 14 : 5

raki99 · Answer

let, total people 100
women=80
men=20
women 50 year or less = 80*30%
---------------------------=24
so, required ratio= 24:20
-------------------= 6:5

exc4libur · Answer

Find the ratio of  \frac{Woman<50}{Men}=\frac{0.3*80}{20}=\frac{24}{20}=6:5

(C) is the answer.

AkshdeepS · Answer

Say, Total people in the room = 100

80% are women = 80 women (Given)

So, men = 100 - 80 = 20 men

70% of the women in a room are over 50 years old = 80*70/100 = 56 women

Therefore, no. of women <=50 years = 80 - 56 = 24

the ratio of the number of women 50 years old or less to the number men in the room = 24:20

Answer = 6:5 (C)

niks18 · Answer

Very simple and straight forward solutions have been presented above

. Here's another approach just for academic purpose

Given ratio of women to men = 80:20=4:1 . So women forms 4 parts of the population. it is given 70 % of WOMEN ( 4 parts) are more than 50 years so 30 % of WOMEN ( 4 parts) will be less than or equal to 50 years Hence new ratio = (30 % *4):1=\frac{6}{5}:1=6:5 Option C

MvArrow · Answer

Can you please tell me why I can't get the correct answer?

Total number of people = X
Total Woman = 4X/5
Total Men = X/5

Women >50 = (4x/5)(7/10) = 28X/50
Women <50 = 22X/50

Ratio = 22X/50 / X/5 = 11/5 !!

niks18 · Answer

Hi  MvArrow

the highlighted part is incorrect

as you have calculated Women>50 as 28x/50

so women less than 50 has to be =4x/5-28x/50=12x/50

you have subtracted women>50 from the total population which is incorrect

MvArrow · Answer

Thanks a lot! Stupid error

ouch! Now I fully understand

Abhishek009 · Answer

Let there be 100 People in the room.

Total women in the room is  80  & Total Men in the Room is  20

Women in a room over 50 years old =  56

Women in a room less than 50 years old is  80 - 56  =  24

So, ratio of the number of women 50 years old or less to the number men in the room is  24 : 20  =  6 : 5 , answer must be (C)

adiitya · Answer

Ratio = No. of female less than or equal to 50yrs/total No of male
If:
Total number of people = 100
Then:
Total number of female = 80
Total number of male = 20
Females who are greater than 50yrs = 70% of all females
Females who are less than or equal to 50yrs = 30% of all females = 0.3*80

So, ratio = 0.3*80/20 = 0.3*4 = 1.2 = 6/5 = hence, C
Hope it helps.

If 70% of the women in a room are over 50 years old and 80% of the peo

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If 70% of the women in a room are over 50 years old and 80% of the peo

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards