Question

In a group of 20 singers and 40 dancers, 20% of the singers are less than 25 years old and 40% of the entire group are under 25 years of age. What percentage of the dancers are under 25 years of age?

Answer 1

Hint:Here, in this given question, we must first of all find the number of singers which consists of 20% of the singers. Then we should find the number of people that are 40% of the total group. From this, we have to subtract the number of people in 20% of the singers to get the number of dancers that are under the age of 25 years. Thereafter, we may find the required percentage.

Complete step-by-step answer:
In this given question, we are provided that in a group of 20 singers and 40 dancers, 20% of the singers are less than 25 years old and 40% of the entire group are under 25 years of age.
We are asked to find the percentage of the dancers are under 25 years of age.
Now, $ 20\%\text{ of }20=\dfrac{20}{100}\times 20=4 $
So, 4 singers are under the age of 25 years.
Now, the total group contains 20+40=60 members.
\[40\%\text{ }of\text{ }60=\dfrac{40}{100}\times 60=24\]
So, 24 of the total group are less than 25 years of age.
This means that 24-4=20 dancers are the age of 25 years.
So, $ \dfrac{20}{40}\times 100=50\% $
Therefore, we have got our answer as 50% of the dancers are under 25 years old.

Note: In this sort of question, we must be careful while considering the percentage of the total group, the members will be the sum of all the respective groups as per given information. The possible mistake that can be committed here is by not considering that we have been given that 40% of “entire group” are under 25 years of age and we have to find % of dancers under 25 years of age. Then we might end up writing 24 and then computing the final answer.