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# Jon and his twin sister, together with their 3 younger brothers

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Jon and his twin sister, together with their 3 younger brothers  [#permalink]

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04 Oct 2018, 09:51
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Jon and his twin sister, together with their 3 younger brothers, are wrapping presents. Each of the younger brothers can wrap presents at $$\frac{1}{4}$$ 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?

$$A)\frac{2}{11} B)\frac{4}{11} C)\frac{8}{11} D)\frac{11}{8} E)\frac{11}{2}$$

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Jon and his twin sister, together with their 3 younger brothers  [#permalink]

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04 Oct 2018, 10:45
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Abhi077 wrote:
Jon and his twin sister, together with their 3 younger brothers, are wrapping presents. Each of the younger brothers can wrap presents at $$\frac{1}{4}$$ 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?

$$A)\frac{2}{11} B)\frac{4}{11} C)\frac{8}{11} D)\frac{11}{8} E)\frac{11}{2}$$

Each of the younger brothers can wrap presents at $$\frac{1}{4}$$ of the rate that Jon and their older sister can each wrap 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

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Re: Jon and his twin sister, together with their 3 younger brothers  [#permalink]

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04 Oct 2018, 11:18
Hi chetan2u ,
You have written "both jon and the sister are equal to 4 younger brothers combined in work.."
But we have 3 younger brothers.
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Re: Jon and his twin sister, together with their 3 younger brothers  [#permalink]

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04 Oct 2018, 14:20
Abhi077 wrote:
Jon and his twin sister, together with their 3 younger brothers, are wrapping presents. Each of the younger brothers can wrap presents at $$\frac{1}{4}$$ 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.
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Re: Jon and his twin sister, together with their 3 younger brothers   [#permalink] 04 Oct 2018, 14:20
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