A company has 40 employees whose names are listed in a certain order. In 2022, the average bonus of the first 30 employees was Rs. 36,000, of the last 30 employees was Rs. 56,000, and of the first 10 and last 10 employees together was Rs. 46,000. In the next year, the average bonus of the first 10 employees doubled, the average bonus of the last 10 employees became three times its previous value, and the bonuses of the remaining 20 employees remained unchanged. Then, the average bonus, in rupees, of all 40 employees together in 2023 was:
Answer and solution
Correct answer: C
Solution
Answer: C — 88,000
1. Divide the 40 employees into three groups:
2. First 10 employees = F
Middle 20 employees = M
Last 10 employees = L
3. Work in thousands of rupees.
4. The average of the first 30 employees is 36,000:
5. F + M = 30 × 36 = 1080 ...(1)
6. The average of the last 30 employees is 56,000:
7. M + L = 30 × 56 = 1680 ...(2)
8. The average of the first 10 and last 10 together is 46,000:
9. F + L = 20 × 46 = 920 ...(3)
10. Add equations (1) and (2), then subtract equation (3):
11. 2M = 1080 + 1680 − 920
2M = 1840
M = 920
12. Now:
13. F = 1080 − 920 = 160
L = 1680 − 920 = 760
14. In 2023:
The first 10 employees' bonus doubles, so their total becomes 2 × 160 = 320.
The middle 20 employees' total remains 920.
The last 10 employees' total becomes 3 × 760 = 2280.
15. New total bonus = 320 + 920 + 2280 = 3520 thousand.
16. Average = 3,520,000 ÷ 40 = Rs. 88,000.
17. Answer: Rs. 88,000.
Why this method works:
F, M, L denote total bonuses of groups of 10,20,10 employees, not their averages. The first-30 and last-30 groups overlap in the middle 20, which is why adding those totals counts M twice.
Independent check and common trap:
Original group averages are ₹16,000,₹46,000,₹76,000. Next-year totals are ₹320,000,₹920,000,₹2,280,000, summing to ₹3,520,000. Divide by all 40 employees, not by three groups of unequal size.
Apply: In thousands: F+M=1080, M+L=1680, F+L=920. M=920, F=160, L=760. New total 2F+M+3L=3520; divide 40 →88 thousand.
Check: Original group averages are ₹16,000,₹46,000,₹76,000. Next-year totals are ₹320,000,₹920,000,₹2,280,000, summing to ₹3,520,000. Divide by all 40 employees, not by three groups of unequal size.
1. Divide the 40 employees into three groups:
2. First 10 employees = F
Middle 20 employees = M
Last 10 employees = L
3. Work in thousands of rupees.
4. The average of the first 30 employees is 36,000:
5. F + M = 30 × 36 = 1080 ...(1)
6. The average of the last 30 employees is 56,000:
7. M + L = 30 × 56 = 1680 ...(2)
8. The average of the first 10 and last 10 together is 46,000:
9. F + L = 20 × 46 = 920 ...(3)
10. Add equations (1) and (2), then subtract equation (3):
11. 2M = 1080 + 1680 − 920
2M = 1840
M = 920
12. Now:
13. F = 1080 − 920 = 160
L = 1680 − 920 = 760
14. In 2023:
The first 10 employees' bonus doubles, so their total becomes 2 × 160 = 320.
The middle 20 employees' total remains 920.
The last 10 employees' total becomes 3 × 760 = 2280.
15. New total bonus = 320 + 920 + 2280 = 3520 thousand.
16. Average = 3,520,000 ÷ 40 = Rs. 88,000.
17. Answer: Rs. 88,000.
Why this method works:
F, M, L denote total bonuses of groups of 10,20,10 employees, not their averages. The first-30 and last-30 groups overlap in the middle 20, which is why adding those totals counts M twice.
Independent check and common trap:
Original group averages are ₹16,000,₹46,000,₹76,000. Next-year totals are ₹320,000,₹920,000,₹2,280,000, summing to ₹3,520,000. Divide by all 40 employees, not by three groups of unequal size.
G Strategy shortcut
Spot: Arithmetic – Averages.Apply: In thousands: F+M=1080, M+L=1680, F+L=920. M=920, F=160, L=760. New total 2F+M+3L=3520; divide 40 →88 thousand.
Check: Original group averages are ₹16,000,₹46,000,₹76,000. Next-year totals are ₹320,000,₹920,000,₹2,280,000, summing to ₹3,520,000. Divide by all 40 employees, not by three groups of unequal size.
G Strategy: Spot: Arithmetic – Averages. Apply: In thousands: F+M=1080, M+L=1680, F+L=920. M=920, F=160, L=760. New total 2F+M+3L=3520; divide 40 →88 thousand. Check: Original group averages are ₹16,000,₹46,000,₹76,000. Next-year totals are ₹320,000,₹920,000,₹2,280,000, summing to ₹3,520,000. Divide by all 40 employees, not by three groups of unequal size.