# Difficult Averages Solved QuestionAptitude Discussion

 Q. $40\%$ of the employees in a factory are workers. All the remaining employees are executives. The annual income of each worker is Rs. 390. The annual income of each executive is Rs. 420. What is the average annual income of all the employees in the factory together?
 ✖ A. 390 ✖ B. 405 ✔ C. 408 ✖ D. 415

Solution:
Option(C) is correct

Let $e$ be the number of employees.

We are given that $40\%$ of the employees are workers. Now, $40\%$ of $e$ is

$\dfrac{40}{100}\times e=0.4e$

Hence, the number of workers is $\dfrac{2e}{5}$

All the remaining employees are executives, so the number of executives equals

(The number of Employees)–(The number of Workers)

$=e-\dfrac{2e}{5}$

$=\dfrac{3e}{5}$

The annual income of each worker is Rs. 390. Hence, the total annual income of all the workers together is:

$=\dfrac{2e}{5}\times 390$

$=156e$

Also, the annual income of each executive is Rs. 420. Hence, the total income of all the executives together is

$=\dfrac{3e}{5}\times 420$

$=252e$

Hence, the total income of the employees is :

$156e+252e=408e$.

The average income of all the employees together equals

$\dfrac{\text{The total income of all the employees}}{\text{The number of employees}}$

$=\dfrac{408e}{e}$

$=408$

Edit: Check shortcut method by Fara.

## (9) Comment(s)

Ishwar
()

390 & 415 can not be the answers as they are way too unrealistic.

415 is average of 420 and 390. So for 415 to be the answer workers and executives need to be in equal proportion.

Hence only answer can be 408.

NITHIN RAJ
()

U don't need these at all

℅. Ratio

40℅. 2. 390

60%. 3. 420

Take assumed average 400

400+((-20+60)/5)

408

100%. 5

Vivek Sharma
()

ratio , workers:employees=2:3

so (2*390+3*420)/(2+3)= 408

Sri Devi
()

(40/100)(390)+(60/100)(420) = 408

since 40% of the employees get Rs.390 and the rest, i.e., 60% of the employees get Rs.420. :)

UniQue
()

take total number of workers and executives as 100

then total salary of workers=40*390

total salary of executives=60*420

avg. salary of all=(40*390+60*420)/100=408

Pushpendra
()

it can be done by taking 100 as base too same as above

Herat Patel
()

40% of workers each one's salary = 390 so total salary=(390*40)= 15600

60% of executives each one's salary=420 so total salary=(420*60)= 25200

(15600+25200)/100

40800/100

ANS : 408

Sudheer Mvr
()

take total as 100; ex -60,em -40-----avg = 40*390+60*420/100 = 408

Fara
()

Here is a simple method:

Suppose there are 10 total employees, 40% are worker, meaning 4 workers are there and remaining 6 are executives.

So the average will be:

$\dfrac{4(390)+6(420)}{10} = 408$

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