GATE2014 AE: GA-9

Question

One percent of the people of country $X$ are taller than $6$ ft. Two percent of the people of country $Y$ are taller than $6$ ft. There are thrice as many people in country $X$ as in country $Y.$ Taking both countries together, what is the percentage of people taller than $6$ ft?

• A. $3.0$
• B. $2.5$
• C. $1.5$
• D. $1.25$

Answer 1

Let the no. people in $Y=a.$

No. of people in $Y$ greater than  $6$ feet $=\dfrac{2a}{100}$
No. of people in $X=3a$
No. of people in $X$ greater than $6$ feet $=\dfrac{3a}{100}$
Total number of people greater than $6$ feet $=\dfrac{2a}{100}+\dfrac{3a}{100}=\dfrac{5a}{100}$

Total number of people $=a+3a=4a.$
Percentage of people in $X+Y$ greater than $6$ feet $=\left(\dfrac{5a}{100}\div {4a}\right) \times{100}=1.25 \%$

Correct Answer: $D$

Answer 2

given country X population is 3 times more than country Y .

so assume country Y has population =100

therefore ,country x population =300 .

now  calculate people who are >6ft i.e 1% of 300 =3 and 2% of 100=2

people who are (>6ft ) in country X+Y = 3+2 =5

percentage =(5/(total population in X+Y=400))*100=1.25

therefore answer is 1.25