The sum of three positive numbers is 339. If the ratio of the first number to the second number is 3:7, and that of the second number to the third number is 5:9, then the second number is:

Let the three positive numbers be A,B, and C.
Given ratios:

B
A
​
=
7
3
​
and
C
B
​
=
9
5
​

To combine these ratios, we need to make the term corresponding to B equal in both ratios. The LCM of 7 and 5 is 35.

Multiply the first ratio by 5:

A:B=3×5:7×5=15:35
Multiply the second ratio by 7:

B:C=5×7:9×7=35:63
Now, the combined ratio is:

A:B:C=15:35:63
Let the numbers be 15k,35k, and 63k. Their sum is given as 339:

15k+35k+63k=339
113k=339
k=
113
339
​
=3
The second number (B) is:

B=35k=35×3=105