Question

Two-third employees of a company ane graduates and the rest are non-graduates. If 3/16 of the graduate employees and of the one-fourth of the others are temporary employees and the total number of permanent employees is 1045, then 5/12 total employees exceeds the number of non-graduate employees by:

a. 132
b. 124
c. 120
d. 110​

Answer 1

Given :

The number of graduate employee = $\dfrac{2}{3}$ of total

The number of non-graduate employee = $\dfrac{1}{3}$ of total

Number of temporary employee = $\dfrac{3}{16}$ of graduate + $\dfrac{1}{4}$ of non-graduate

The total number of permanent employees = 1045

To Find :

$\dfrac{5}{12}$ total employees exceeds the number of non-graduate employees by

Solution :

Let The Total number of employees = n

∴ The number of graduate employee = $\dfrac{2}{3}$ of total =  $\dfrac{2}{3}$  × n =  $\dfrac{2n}{3}$

The number of non-graduate employee = $\dfrac{1}{3}$ of total =  $\dfrac{1}{3}$  × n =  $\dfrac{n}{3}$

Again

Number of temporary employee = $\dfrac{3}{16}$ of graduate + $\dfrac{1}{4}$ of non-graduate

                                                      = $\dfrac{3}{16}$ ×  $\dfrac{2n}{3}$ +  $\dfrac{1}{4}$  ×  $\dfrac{n}{3}$

                                                       = $\dfrac{n}{8}$ + $\dfrac{n}{12}$

                                                      = $\dfrac{3n+2n}{24}$

                                                     = $\dfrac{5 n}{24}$

Again

∵ total number of permanent employees = 1045

∴ total number of temporary employees = n - 1045

i.e n - 1045  =  $\dfrac{5 n}{24}$

Or, 24 n - 25080 = 5 n

Or, 24 n - 5 n = 25080

Or,  21 n = 25080

∴         n = $\dfrac{25080}{21}$

i.e       n = 1194

Again

$\dfrac{5}{12}$ total employees exceeds the number of non-graduate employees by = $\dfrac{5}{12}$ × n -  $\dfrac{n}{3}$  = $\dfrac{5}{12}$ × n -  $\dfrac{n}{3}$

                = $\dfrac{5n-4n}{12}$

                = $\dfrac{n}{12}$

                = $\dfrac{1194}{12}$ = 99.5 ≈ 100

Hence, $\dfrac{5}{12}$ total employees exceeds the number of non-graduate employees by 100  . Answer