In a theatre group, the ratio of males to females is 2:3. On one Tuesday training, 10 male members were absent and six new female members joined the group as guests for the day. If on this day the rat

Let $M$ be the initial number of male members and $F$ be the initial number of female members.
The initial ratio of males to females is $2:3$.

This means $M = 2k$ and $F = 3k$ for some constant $k$.

On Tuesday, 10 male members were absent, so the number of males present was $M - 10$.
Six new female members joined, so the number of females present was $F + 6$.

On this day, the ratio of males to females was $1:3$.

Cross-multiply:

Subtract $3k$ from both sides:

Add 30 to both sides:

Divide by 3:

Initial number of males $M = 2k = 2(12) = 24$.
Initial number of females $F = 3k = 3(12) = 36$.

The total number of regular members is $M + F$.
Total regular members $= 24 + 36 = 60$.

The group has 60 regular members.

The final answer is 60.