Question

In RSM camp, there are four counselors for every fifty seven students and three teachers for every five counselors.

Write the ratio of students to counselors to teachers, respectively.

Answer 1

Students : Counselors : Teachers = 285: 20 : 12

Explanation:

In the camp, the ratio of:

( C: S ) Counselors : Students is 4 : 57

( T: C ) Teachers : Counselors is 3 : 5

To determine the ratio of - Students : Counselors : Teachers

Here given - C : S = 4 : 57

Multiplying both sides by 5, we get

C: S = 4 x 5 : 57 x 5 = 20 : 285

So, for every 20 counselors, there are 285 students ...... (1)

Similarly, given Teachers : Counselors is 3 : 5

Multiplying both sides by 4, we get

T : C = 3 x 4 : 5 x 4 = 12 : 20

So, for every 12 teachers, there are 20 Counselors ...... (2)

Hence, in both equation 1 and 2 the number of counselors is same = 20 .

Hence, both the ratios acne be combined.

So we get C : S = 20 : 285 and T : C = 12: 20

Inverting the values

⇒ S : C = 285 : 20 and C : T = 20 : 12

or, S : C : T = 285: 20 : 12

or, Students : Counselors : Teachers = 285: 20 : 12

Hence, for every 285 students there are 20 counselors and 12 teachers.