In a medical institute, the strength of the students in the first two classes are in the ratio of 8:17. The ratio of the number of students in the second and the third classes is 2:3. What is the average of the number of students in the first and third classes, if the number of students in the second class is 612?

Let the three classes be denoted as C
1
​
, C
2
​
, and C
3
​
.
Given ratios:

C
2
​

C
1
​

​
=
17
8
​

C
3
​

C
2
​

​
=
3
2
​

To combine the ratios, let's make the term for C
2
​
common by multiplying the first ratio by 2 and the second ratio by 17:

C
1
​
:C
2
​
=8×2:17×2=16:34
C
2
​
:C
3
​
=2×17:3×17=34:51
So, the combined ratio is:

C
1
​
:C
2
​
:C
3
​
=16:34:51
We are given that the number of students in the second class C
2
​
=612:

34k=612⟹k=
34
612
​
=18
Now, we calculate the strength of the first and third classes:

C
1
​
=16×18=288
C
3
​
=51×18=918
The average of the number of students in the first and third classes is:

Average=
2
C
1
​
+C
3
​

​
=
2
288+918
​
=
2
1206
​
=603