Question

225
In a class 20% of students are below 14 years of age. Out of the remaining students 10% are
of the age 14-15 years and ratio of students who are between 15-16 years of age to student
above 16 years of age is 3:2. If the number of students who are above 16 years is 72, what is
the total number of students in the class?
200
250
300
400​

Answer 1

Answer:

250 students ................

Answer 2

Answer:

The total number of students in the class is 250.

Step-by-step explanation:

From the given,

The percentage of students below 14 years of age is 20% of the total.

The percentage of students of age 14-15 years in the remaining is 10%.

The ratio of the number of students who are between 15-16 years and above 16 years is 3:2.

The number of students who are above 16 years of age is 72.

To find:

The total number of students in the class.

Step 1 of 3:

Let N be the total number of students in the class.

Thus from the given, we can write the data

The number of students below 14 years of age is,

$20\%= \frac{20}{100}N\\=0.2N$

The remaining number of students will be,

$N-\frac{20}{100}N=\frac{80}{100} N$

The number of 10% students in the remaining of the age 14-15 years is,

$\frac{10}{100}(\frac{80}{100}N)=0.08N$

Step 2 of 3:

Let x represent the number of students who are between 15-16 years of age.

Thus, the ratio of the students who are between 15-16 years of age and above 16 years of age can be written as,

Number of students of 15-16 years: Number of students above 16 years,

$\frac{3}{2} = \frac{x}{72}$

Solving for x, we get

$x=72(\frac{3}{2}) \\=36(3)\\=108$

Step 3 of 3:

The total number of students is given by adding the number of students of ages 14, 14-15, 15-16, and above 16 years.

$N=0.2N+0.08N+108+72\\N=0.28N+180\\N-0.28N=180\\0.72N=180\\N=\frac{180}{0.72}\\ N=250$

Final answer:

Hence, the total number of students in the class is 250.