Question

A company has 40 employees whose names are listed in a certain order. In the year 1925, the average bonus of the first 30 employees was Rs. 40000, of the last 30 employees was Rs. 60000, and of the first 10 and last 10 employees together it was Rs. 50000. Next year, the average bonus of the first 10 employees increased by 100%, of the last 10 employees increased by 200% and of the remaining employees was unchanged. Then, the average bonus, in Rupees, of all the 40 employees together in the year 1926 would have been:

• A. 90000
• B. 78000
• C. 85000
• D. 80000
• E. 60000

Hint:

Be careful with percentage increases: "increased by 100%" means doubled; "increased by 200%" means tripled. Always identify the base value (the original averag(e) correctly.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
We must divide the employees into three groups: group A (1-10), group B (11-30), and group C (31-40).
Step 2: Key Formula or Approach:
Total Sum \( = \) Average \( \times \) Count.
Step 3: Detailed Explanation:
Let \( S_a, S_b, S_c \) be the total bonuses of the three groups in 1925.
1. \( S_a + S_b = 30 \times 40000 = 1200000 \).
2. \( S_b + S_c = 30 \times 60000 = 1800000 \).
3. \( S_a + S_c = 20 \times 50000 = 1000000 \).
Adding (1) and (2): \( S_a + 2S_b + S_c = 3000000 \).
Subtracting (3): \( 2S_b = 2000000 \Rightarrow S_b = 1000000 \).
From (1), \( S_a = 200000 \). From (2), \( S_c = 800000 \).
In 1926:
Group A increases by 100%: \( S_a' = 200000 + 200000 = 400000 \).
Group C increases by 200%: \( S_c' = 800000 + (2 \times 800000) = 2400000 \).
Group B remains unchanged: \( S_b' = 1000000 \).
Total bonus in 1926 \( = 400000 + 1000000 + 2400000 = 3800000 \).
Average \( = 3800000 / 40 = 95000 \).
Step 4: Final Answer:
The average bonus in 1926 is 95000.