CAT 2001 — QA Question 11
Two men X and Y started working for a certain company at similar jobs on January 1, 1950. X asked for an initial salary of Rs. 300 with an annual increment of Rs. 30. Y asked for an initial salary of Rs. 200 with a rise of Rs. 15 every six months. Assume that the arrangements remained unaltered till December, 1959. Salary is paid on the last day of the month. What is the total amount paid to them as salary during the period?
Answer & solution
Rs. 93,300
- B
Rs. 93,200
- C
Rs. 93,100
- D
None of these
X’s salary = [3600] + [3600 + 30 × 12] + [3600 + 30 × 12 × 2] + … + [3600 + 30 × 12 × 9]
= [3600 × 10] + [30 × 12(1 + 2 + 3 + … + 9)]
= Rs. 52,200
Y’s salary = [1200 × 20] + [15 × 6(1 + 2 + 3 + … + 19)]
= Rs. 41,100
∴ Sum of X and Y’s salary = Rs. 52,200 + Rs. 41,100 = Rs. 93,300
Hence, option (a).
Alternatively,
X starts at a salary of 300 and ends at a salary = 300 + 30 × 9 = 570
∴ X's average salary =
Y starts at a salary of 200 and ends at a salary = 200 + 15 × 19 = 485
∴ Y's average salary =
∴ X and Y’s total salary = (435 + 342.5) × 12 × 10 = Rs. 93,300
Hence, option (a).