Set A Solutions

A1. Sum = 24+36+18+42+30 = 150. Average = 150/5 = 30. Answer: (b) 30

A2. Average of first n natural numbers = (n+1)/2 = 51/2 = 25.5. Answer: (c) 25.5

A3. Average of first n even numbers = n+1 = 30+1 = 31. Answer: (c) 31

A4. Average of first n odd numbers = n = 25. Answer: (c) 25

A5. Average of squares of first n natural numbers = (n+1)(2n+1)/6 = (11)(21)/6 = 231/6 = 38.5. Answer: (d) 38.5

A6. Average of cubes of first n natural numbers = n(n+1)²/4 = 9×(10)²/4 = 9×100/4 = 900/4 = 225. Answer: (c) 225

A7. Weighted average = (40×60 + 60×70)/(40+60) = (2400+4200)/100 = 6600/100 = 66. Answer: (c) 66

A8. Equal distance → Average speed = 2xy/(x+y) = 2×40×60/(40+60) = 4800/100 = 48 km/h. Answer: (b) 48 km/h

A9. Equal time (3 hrs each) → Average speed = (40+60)/2 = 50 km/h. Verify: total distance = 120+180=300 km, total time = 6 hrs, average = 50 km/h ✓. Answer: (b) 50 km/h

A10. New weight = Old weight + n×d = 50 + (10×2) = 50+20 = 70 kg. Answer: (c) 70 kg

A11. Teacher’s age = New average×(n+1) − Old average×n = 12.5×31 − 12×30 = 387.5 − 360 = 27.5 years. Answer: (c) 27.5 years

A12. When one number increases by 15, the total increases by 15, so the average increases by 15/5 = 3. New average = 20+3 = 23. Answer: (c) 23

A13. Since the composition (2 people, no one joins/leaves) doesn’t change, average age after 6 years = 28+6 = 34 years. Answer: (c) 34 years

A14. Assume A = 47. Deviations: 41−47=−6, 43−47=−4, 47−47=0, 49−47=+2, 53−47=+6. Sum of deviations = −6−4+0+2+6 = −2. Average = 47 + (−2/5) = 47−0.4 = 46.6. Answer: (c) 46.6

A15. First 15 multiples of 8: 8,16,…,120. Average = (First+Last)/2 = (8+120)/2 = 128/2 = 64. Answer: (c) 64

A16. Sum of 6 numbers = 22×6 = 132. Sum of remaining 5 numbers = 20×5 = 100. Excluded number = 132−100 = 32. Answer: (c) 32

A17. Average of an AP = (First term + Last term)/2 = (20+50)/2 = 70/2 = 35. Answer: (c) 35

A18. Weighted average = (15×100 + 25×140)/(15+25) = (1500+3500)/40 = 5000/40 = 125. Answer: (b) ₹125

A19. Since the new number is 54 and the average increased by 2 over 12 numbers, use N = O + n×d, so O = N − n×d = 54 − 12×2 = 54−24 = 30. Answer: (c) 30

A20. Equal time (2 hrs each) → Average speed = (12+18)/2 = 30/2 = 15 km/h. Answer: (b) 15 km/h