Average monthly income of ‘A’ working people from a locality was found to be Rs. 20000. If 25 senior citizens retire the following year and 10 freshers get job, the average monthly income will go down by Rs. 1000. Instead if, 30 senior citizens retire and 30 freshers get job, their average monthly income increase by Rs. 1950. If all the senior citizens got a salary of Rs. 30000 and all freshers are paid the same salary. What is the initial number of working people?

Average monthly income of ‘A’ working people from a locality was found to be Rs. 20000. If 25 senior citizens retire the following year and 10 freshers get job, the average monthly income will go down by Rs. 1000. Instead if, 30 senior citizens retire and 30 freshers get job, their average monthly income increase by Rs. 1950. If all the senior citizens got a salary of Rs. 30000 and all freshers are paid the same salary. What is the initial number of working people? Correct Answer 100

Let the salary of a fresher be y

Initially, average monthly income of ‘A’ working people = 20000

∴ Total income of ‘A’ working people = 20000 × A

Now 25 senior citizens retire and 10 freshers get job.

⇒ Total number of working people = A + 10 - 25 = A - 15

⇒ Average income after retirement of 25 senior citizens and 10 freshers getting job = 20000 – 1000 =19000

⇒ Total income of ‘A - 15’ working people = 19000 × (A - 15)

This total income = Initial income – Income of 25 senior citizens+ Income of 10 freshers

⇒ 19000(A - 15) = 20000A – 25 × 30000 + 10y

⇒ 19000A - 285000 = 20000A – 750000 + 10y

⇒ -285000 + 750000 = (20000A – 19000A) + 10y

⇒ 465000 = 1000A + 10y       ---- 1

Now 30 senior citizens retire and 30 freshers get job.

⇒ Total number of working people = A – 30 + 30 = A

⇒ Average income after retirement of 30 senior citizens and 30 freshers getting job = 20000 + 1950 = 21950

⇒ Total income of ‘A’ working people = 21140 × A

This total income = Initial income – Income of 30 senior citizens+ Income of 30 freshers

⇒ 21950A = 20000A – 30 × 30000 + 30y

⇒ 1950A = -900000 + 30y

⇒ -900000 = 1950A – 30y

⇒ -300000 = 650A – 10y       ---- 2

Adding eq 1 and 2

⇒ 465000 – 300000 = 1000A + 650A

⇒ 165000 = 1650A

∴ A = 100