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ratio problem

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ratio problem

by mohammadali » Thu Oct 20, 2011 10:09 am
xyz is an it company with 90 employees who all are developers. the ratio of developers working on java to php is 7:3. ratio of php to java and php is 6:4. the ratio of php to developers not working on java and php is 3:1

1) how many developers work only on java
2) """ """ work only on php
3) "" "" both java and php
4
5) how many neither work in java nor php
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by avik.ch » Fri Oct 21, 2011 11:42 am
I couldn't understand your problem. How can a GMAT PS has 5 questions ?? Moreover what is 4 - blank .
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by krishnakumar.ks » Fri Oct 21, 2011 12:23 pm
mohammadali wrote:xyz is an it company with 90 employees who all are developers. the ratio of developers working on java to php is 7:3. ratio of php to java and php is 6:4. the ratio of php to developers not working on java and php is 3:1

1) how many developers work only on java
2) """ """ work only on php
3) "" "" both java and php
4
5) how many neither work in java nor php
Let us assume
j = number of developers who work only on java
p = number of developers who work only on php
b = number of developers who work on both java and php
n = number of developers who doesn't work on both java and php

Step 1 : (j+b)/(p+b) = 7/3 and on solving it gives j = (7b+4p)/3 ------------(i)
Step 2 : (p+b)/(b) = 6/4 and on solving gives b=2p --------------------------(ii)
Step 3 : (p+b)/n = 3/1. Sub the value of b from ii and you will get n = b ---- (iii)
Step 4 : Substitute the value of b in (i) and it gives j = 5p------ (iv)

Now, given that j+p+b+n = 90 and substituting the values from above,
5p + p + 2p + p = 90 => p=10. With this value of p you can get the other values and all the answers for your question.

In fact this can be solved much quicker by venn-diagram-approach.
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