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Two buses and a van were employed to transport a class of students on

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Two buses and a van were employed to transport a class of students on [#permalink]

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New post 07 May 2015, 14:20
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Two buses and a van were employed to transport a class of students on a field trip. 3/5 of the class boarded the first bus. 2/3 of the remaining students boarded the second bus, and the rest of the students boarded the van. When the second bus broke down, 1/2 of the students on the second bus boarded the first bus. What fraction of the class was on board the first bus?
a) 1/2
b) 2/3
c) 11/15
d) 23/30
e) 4/5
[Reveal] Spoiler: OA

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Re: Two buses and a van were employed to transport a class of students on [#permalink]

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New post 07 May 2015, 16:21
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This is a pure ratio question (we aren't given any numbers for anything), so you can just choose any starting number you like, and use it to solve the problem. The best number to pick is almost always the product of all the denominators of your fractions, so here we could start with 30 students. Then we have:

• 3/5 of these, or 18 students, board the first bus
• there are 12 students left. 2/3 of these, or 8 students, board the second bus
• this bus breaks down, and 1/2 of the 8 students, or 4 students, board the first bus
• the first bus now contains 22 out of the original 30 students, so the answer is 22/30 = 11/15
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Re: Two buses and a van were employed to transport a class of students on [#permalink]

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New post 08 May 2015, 01:54
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Presenting the algebraic way of the solution

Given:
We are given that for a field trip \(\frac{3}{5}\) of the total students boarded the first bus and \(\frac{2}{3}\) of the remaining students boarded the second bus while the rest boarded the van. Also, when the second bus broke down \(\frac{1}{2}\) of the students on the second bus boarded the first bus. We are asked to find the ratio of final number of the students on the first bus to the total students.

Approach
Since, we need to find the ratio of two things, we have to express them in either constants or in the same terms. Since we don't have any information about the exact number of students we will try to express them in the same terms.

We are given relations between the total number of students and the students who boarded the buses and the van. We will use this relation to find out the required ratio.

Working Out
Let's assume total number of students to be \(x\).

Students who boarded the first bus = \(\frac{3x}{5}\)

Students who boarded the second bus = \(\frac{2}{3}\) of remaining students = \(\frac{2}{3}\) * (Total Students - Students who boarded the first bus) = \(\frac{2}{3}\) *( \(x- \frac{3x}{5}\)) = \(\frac{4x}{15}\)

We don't need to find the number of students who boarded the van as it is not being used anywhere.

No. of students of the second bus who boarded the first bus = \(\frac{1}{2} *(\frac{4x}{15}) = \frac{2x}{15}\)

Hence, total number of students in the first bus = original number of students in the first bus + students from second bus who boarded the first bus = \(\frac{3x}{5} + \frac{2x}{15} = \frac{11x}{15}\)

Now, we need to find the ratio of number of students in the first bus to that of the total students which can be written as \(\frac{11x}{15x} = \frac{11}{15}\) which is our answer.

Hope its clear!

Regards
Harsh
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Re: Two buses and a van were employed to transport a class of students on [#permalink]

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Re: Two buses and a van were employed to transport a class of students on [#permalink]

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New post 29 Apr 2017, 08:03
zxcvbnmas wrote:
Two buses and a van were employed to transport a class of students on a field trip. 3/5 of the class boarded the first bus. 2/3 of the remaining students boarded the second bus, and the rest of the students boarded the van. When the second bus broke down, 1/2 of the students on the second bus boarded the first bus. What fraction of the class was on board the first bus?
a) 1/2
b) 2/3
c) 11/15
d) 23/30
e) 4/5


We can let the total number of students = n.

(3/5)n students boarded the first bus and 2/3((2/5)n) = (4/15)n students boarded the second bus.
When the second bus broke down, 1/2 the students boarded the first bus. Thus:

1/2((4/15)n) = (2/15)n students from the second bus boarded the first bus.

So the first bus now has (3/5)n + (2/15)n = (9/15)n + (2/15)n = (11/15)n students.

Answer: C
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Re: Two buses and a van were employed to transport a class of students on   [#permalink] 29 Apr 2017, 08:03
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