by sadmin » Mon Aug 28, 2017 2:02 am
QCS-6
Average - Practice Questions
Q30
Average salary of officers, clerks, and bearers:1200, 450 and 180 respectively.
Average salary of the three classes = Rs 440
Raise in salary in the new scale of pay - officers, clerks, and bearers- 60, 30 and 20 Rs respectively
New monthly average salary= Rs 470
In the initial pay scale:
Initially,
total salary = salary of all officers + salary of all clerks + salary of all bearers
Assume the the number of officers, clerks and bearers to be a,c, and b
thus we have=> 440 (a+b+c) =1200(a) + 450(b) +180(c)
On simplifying the above equation we have : 440a + 440b + 440c = 1200a + 450c + 180b
=> 760a +260 c = 10b => 76 a + 10c = 260b => 76a + c = 26 b................(i)
Similarly, after the new payscale is launched -we can write a similar equation:
total salary = salary of all officers + salary of all clerks + salary of all bearers
Thus we have : 470 (a +b +c) = 1260 a + 480 c + 200 b
=> 790a + 10 c = 270 b => 79a + c = 27 b .............(ii)
From i and ii we have
76a + c = 26 b
79a + c = 27 b .
For such questions , we need to get a and c in terms of b. That is the number of officers and clerks in terms of the number of bearers.
Subtracting i from ii we get:
3a = b or the number of officers = a =b/3 ..........iii
Putting the value of iii in i we get
76 . (b/3) + c = 26b => c =2b/3
Thus the total number of employees = number of officers + number of clerks + number of bearers = b/3+ 2b/3+ b
=> Total employees = 2b
Number of officers = b/3
Percentage of officers = (Number of officers / total of employees ) x 100 = (b/3) /(2b) x 100 = 16.66 % or
Ans option (b)