Jon and his twin sister, together with their 3 younger

[AbhishekRyu]

Jon and his twin sister, together with their 3 younger brothers, are wrapping presents. Each of the younger brothers can wrap presents at 1/4 of the rate that Jon and their older sister can each wrap presents. If all 5 children wrap presents at the same time, in what fraction of the time that it would take Jon and his twin sister to wrap 10 presents together will all 5 children working together take to complete the task?
A) $$\frac{2}{11}$$
B) $$\frac{4}{11}$$
C) $$\frac{8}{11}$$
D) $$\frac{11}{8}$$
E) $$\frac{11}{2}$$

[swerve]

Each of the younger brothers can wraps presents at 1/4 of the rate that Jon and their older sister can each wraps presents.

Means
Both Jon and the sister are equal to 4 younger brothers combined in work.

So, Jon is equal to 4 and sister is equal to 4, thus both combined equal to 4+4 = 8.

Total working hands in terms of capability of younger brothers = 4+4+3=11
Out of these 11, Jon and sister are equivalent of 8 brothers, this they do 8/11 of total work.

Hence, C is the correct answer. Regards!

[fskilnik@GMATH]

Jon and his twin sister, together with their 3 younger brothers, are wrapping presents. Each of the younger brothers can wrap presents at 1/4 of the rate that Jon and their older sister can each wrap presents. If all 5 children wrap presents at the same time, in what fraction of the time that it would take Jon and his twin sister to wrap 10 presents together will all 5 children working together take to complete the task?
A) $$\frac{2}{11} \,\,\,\,\, B) \frac{4}{11} \,\,\,\,\, C) \frac{8}{11} \,\,\,\,\, D) \frac{11}{8} \,\,\,\,\, E) \frac{11}{2}$$

Let´s say Jon (J) is able to wrap 4 presents per minute, and the same is valid for his twin sister (T).
Hence each younger brother (Y) can wrap 1 present per minute.
$$? = \frac{{{\text{Time}}\left( {J \cup T \cup 3Y} \right)}}{{\,{\text{Time}}\left( {J \cup T} \right)\,}}$$
During 1 min: J and T can wrap 8 presents, the whole group (J, T and 3Y) can wrap 11 presents.

The ratio (11/8) is the rate of jobs [per any interval of time] of (J, T and 3Y united) to (J and T united).

Our FOCUS, i.e., the rate of time [per any given job] of (J, T and 3Y united) to (J and T united) is its reciprocal:
$$? = \frac{{{\text{Time}}\left( {J \cup T \cup 3Y} \right)}}{{\,{\text{Time}}\left( {J \cup T} \right)\,}} = \frac{8}{{\,11\,}}$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.