Q 26 Peter and Paul work as managers in different departments of a consulting firm. Paul's salary as a percentage of Peter's salary is equal to Peter's salary as a
percentage of the combined salaries of Paul and Peter. Find Paul's salary as a percentage of Peter's salary?
Ops: A
62%
57%
B.
C
41%
73%
D.
27
Answers
Given : Paul's salary as a percentage of Peter's salary is equal to Peter's salary as a percentage of the combined salaries of Paul and Peter
To find : Paul's salary as a percentage of Peter's salary
Solution:
Paul Salary = A
Peter Salary = B
Total Salary = A + B
Paul's salary as a percentage of Peter's salary
= 100A/B
Peter's salary as a percentage of the combined salaries of Paul and Peter.
= 100B/(A + B)
=> 100A/B = 100B/(A + B)
=> A² + AB = B²
Let say B = 100 so that A will be % of B
=> A² + 100A = 100²
=> A² + 100A - 100² = 0
=> A = (-100 ± √100² - 4(-100²) )/ 2
=> A = (-100 + 100√5)/2 ( can not be - ve hence -ve value ignored)
=> A = 50(√5 - 1)
=> A = 61.8
as B = 100 Hence Paul's salary as a percentage of Peter's salary = 61.8 %
≈ 62 %
Paul's salary as a percentage of Peter's salary = 62 %
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