## Tuesday, 25 October 2011

### Arithmetic-12 (XAT-2010)

There are two types of employees in sun Metals, general graduates and engineers. 40% of the employees in Sun Metals are general graduates, and 75% engineers earn more than Rs 5 lakh/year. If 50% of of the organization’s employees earn more than Rs 5 lakh/year what proportion of the general graduates employed by the organization earn Rs 5 lakh or less?
A. 3/5
B. 3/4
C. 1/2
D. 2/5
E. None of the above

Solution:

40% of the employees are general graduates => 60% of the employees are engineers

Better way out is working out with proportions instead of percentages.

(Note that 40% = 40/100 = 2/5, 60% = 40/100 = 3/5, 75% = 75/100 = ¾)

Proportion of general graduates = 2/5

Proportion of engineers = 3/5

75% engineers earn more than Rs 5 lakh/year
=> Proportion of engineers earning more than Rs 5 lakh/year =3/4 * 3/5 = 9/20
50% of of the organization’s employees earn more than Rs 5 lakh/year
=> Proportion of general graduates earning more than Rs 5 lakh/year = (1/2) - (9/20) = (10/20) – (9/20) = 1/20
=> Proportion of general graduates earning Rs 5 lakh/year or less = (2/5) - (1/20) = (8/20) – (1/20) = 7/20
This proportion is with reference to all employees in the organization.
The proportion w.r.t the general graduates only = (7/20)/(2/5) = (7/20) * (5/2) = 7/8