A company selects an employee at his 25th age and offers salary as Rs.40000 per annum for first 2 years. Afterwards, every year he gets increment of Rs.4000 for next 15 years and his salary become constant till his retirement. If Rs.80,000 is his average salary (throughout his career) then at what age he retires?

• @prashant answer should be 25+27=52
  if you are saying that 17+25 than there is no need to do all this calculation.you can direct find this.
  
• 9 years agoHelpfull: Yes(2) No(0)
• Solution :
  
  Employee's salary for first two years = Rs.40,000 (per annum)
  
  So, the total salary for first two years = Rs.80,000 ...(1)
  
  Given that, his salary increased by Rs.4000(per annum) for next 15 years.
  
  So, salary for next 15 years are 44,000, 48,000, 52,000,...
  Total salary for next 15 years is 44,000 + 48,000 + 52,000,...
  
  Note that, above sequence is an A.P with first term a = 44000, common difference = d = 4000, total number of terms = n = 15.
  We know that, sum of first n terms in A.P = (n/2)[2a+(n-1)d] and nth term = a+(n-1)d
  Therefore, 15th term = 44,000+(15-1)4000 = 1,00,000 ...(2)
  And the sum of 15 terms = 44,000 + 48,000 + 52,000,+... + 1,00,000
  = (15/2)[2x44000 + 14x4000]
  = (15/2)(144000) = 10,80,000 ...(3)
  
  From (1) and (3), the total salary of first 17 years = Rs.80,000 + Rs.10,80,000 = Rs. 11,60,000 ...(4)
  
  Form (2), we have, The salary of 17th year = Rs.1,00,000
  
  That is, till his retirement, his salary = Rs.1,00,000 (per annum) ...(5)
  
  Let the employee works for X more years.
  Then, the total salary for this X years = Rs.1,00,000 x X
  
  And his experience = 17 + X years ...(5)
  
  Given that, the average salary for 17+X years = Rs.80,000
  
  That is, Rs.80,000 = [Rs. 11,60,000 + RS.1,00,000 x X]/(17+X)
  (17+X)80,000 = [11,60,000 + 1,00,000 x X]
  (17+X)8 = [116 + 10X]
  [136-116] = 10X - 8X
  20 = 2X
  X = 10
  
  Therefore, from eqn 5, Employee's experience = 17+10 = 27 years.
  
  Since, he hired at his 25th age,his retirement age will be = 25+17 = 42.
  
  Hence, the answer is 42.
• 9 years agoHelpfull: Yes(0) No(2)