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 By: Tping (offline)  Monday, March 25 2013 @ 07:23 PM CDT (Read 735 times)
Tping

At Station A, the ratio of the number of children to the number of adults on a train was 4:5.
At the next station, 12 children alighted and 10 adults boarded the train.
The ratio of the number of children to the number of adults on the train then became 7:10.
How many children were on the train at first?

Thank you.

Junior

Registered: 01/26/12
Posts: 25

 By: echeewh (offline)  Tuesday, March 26 2013 @ 03:28 AM CDT
echeewh

Hey Tping,

This is a typical <Changed Qtys> question in which any of Model method, Cross-Multiply method or Simultaneous (Parts & Units) method can be used.

Following pls find my worked solution:

Given that both <Before> and <After> ratios and <Changed Qtys> are given, we can use the Cross-Multiply method as shown:

<Before>
C : A
4 : 5

<Process>
C: -12
A: +10

<After>
C : A
7 : 10

(4u - 12) / 7 = (5u + 10) / 10
10 × (4u - 12) = 7 × (5u + 10)
40u - 120 = 35u + 70
40u - 35u --> 120 + 70
5u --> 190
1u --> 38

Number of Children (C) (at first) = 4u --> 4 × 38
= 152

==============

Trust this helps.

Do let me know again if this is different from your Answerkey or if there's further clarification.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

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