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:
J = total who work on Java.
P = total who work on PHP.
B = total who work on both PHP and Java.
N = total who work on neither PHP nor Java.
To combine ratios with a common element, the common element must be represented by the same value in each ratio.
The common element in all of the given ratios is P:
J:
P = 7:3 = 14:
6.
P:B =
6:4.
P:N = 3:1 =
6:2.
Combining the ratios:
J : P : B : N = 14:6:4:2.
To determine values for those who work ONLY on J and ONLY on P, we need to SUBTRACT the developers who work on BOTH:
Only J = total J - both J and P = 14-4 = 10.
Only P = total P - both J and P = 6-4 = 2.
Thus:
Only J : Only P : Both : Neither = 10:2:4:2.
The sum of the elements in the ratio = 10+2+4+2 = 18.
The total number of workers = 90.
Since 90/18 = 5, all of the values in the ratio must be multiplied by a factor of 5:
Only J : Only P : Both : Neither = 10:2:4:2 = 50:10:20:10.
Total = 50+10+20+10 = 90.
Thus:
Only J = 50.
Only P = 10.
Both = 20.
Neither = 10.
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