Answer Posted / kermit rose

Let the number of males be given the name M.
Let the number of females be given the name F.

If 15 females are absent, then M will be twice that of
present females.
This means that M = 2 * (F - 15)

M = 2 * F - 30.

or 2 * F - M = 30.

Now if in addition to the 15 females being absent, we also
have 45 males being absent,

then this gives the equation,

(F - 15) = 5 * (M - 45)

which simplifies to

F - 15 = 5 * M - 225

5 * M - F = 210

Pulling the equations together, we get

5 * M - F = 210
-M + 2 * F = 30

Multiply the first equation by 2, and keep the second
equation as is.

10 * M - 2 * F = 420
- M + 2 * F = 30

Add the equations.

9 * M = 450

M = 50

Verify answer.
Calculate F
from - M + 2 * F = 30
-50 + 2 * F = 30
2 * F = 30 + 50
F = 40.

If 15 females are absent, then number of males will be twice
that of females.
40 - 15 = 25.
50 = 2 * 25. Confirmed.

If also 45 males were absent, then female strength would be
5 times that of males.
Female strength is 25 due to the 15 females being absent.

50 - 45 = 5.
25 = 5 * 5. Confirmed.

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