Set B Solutions

B1. Answer: (b) 16.67% Price increases by r = 20%. Required reduction in consumption = r/(100+r) × 100 = 20/120 × 100 = 16.67%.

B2. Answer: (b) 28% Using successive % change with a = −20, b = −10: Net change = −20 − 10 + (−20 × −10)/100 = −30 + 2 = −28%. Effective discount = 28%.

B3. Answer: (b) 19,800 a = +10 (first year), b = −10 (second year). Net % change = 10 − 10 + (10 × −10)/100 = 0 − 1 = −1%. Population after 2 years = 20,000 × 0.99 = 19,800. (Direct check by multiplication: 20,000 × 1.10 × 0.90 = 20,000 × 0.99 = 19,800 — confirms the −1% net change.)

B4. Answer: (d) −9% a = +30, b = −30. Net change = 30 − 30 + (30 × −30)/100 = 0 − 9 = −9%. (Matches the shortcut: net change = −a²/100 = −900/100 = −9%.) Option (a), 0%, is the classic wrong answer chosen by aspirants who assume an equal increase and decrease cancel out exactly — they never do.

B5. Answer: (c) 1,080 Valid votes = 12,000 × (1 − 0.10) = 12,000 × 0.9 = 10,800. Winner’s votes = 10,800 × 0.55 = 5,940. Loser’s votes = 10,800 × 0.45 = 4,860. Margin = 5,940 − 4,860 = 1,080 votes.

B6. Answer: (c) 20% Let Sanjay = 100. Rahul = 125 (25% more). Difference = 25. Base for “less than Rahul” is Rahul’s value (125). % less = (25/125) × 100 = 20%.

B7. Answer: (b) 450 Pass marks = 150 + 30 = 180. This equals 40% of maximum marks. 0.40 × M = 180 → M = 180/0.40 = 450.

B8. Answer: (d) 32% a = +10, b = +20 (length and breadth, both increases, applied to the area = product). Net % increase in area = 10 + 20 + (10 × 20)/100 = 30 + 2 = 32%.

B9. Answer: (b) 0% (no change) a = −20 (workers reduced), b = +25 (wage per worker increased). Total wage bill = workers × wage per worker. Net change = −20 + 25 + (−20 × 25)/100 = 5 − 5 = 0%. No change in total wage bill. This is a good example of how a positive “5%” from adding the two changes directly is exactly cancelled by the −5% cross-term, reinforcing why the ab/100 term can never be dropped from the successive-change formula.

B10. Answer: (b) ₹19,800 New salary = 20,000 × 1.10 × 0.90 = 20,000 × 0.99 = ₹19,800. (Confirms the “same % up then down” shortcut: net change = −(10²)/100 = −1%; 20,000 × 0.99 = 19,800.)

B11. Answer: (c) 60% Let initial income = 100, so initial expenditure = 50 (50% of income). New income = 100 × 1.10 = 110. New expenditure = 50 × 1.32 = 66. New expenditure as % of new income = (66/110) × 100 = 60%.

B12. Answer: (c) 5% profit Let cost price = 100. Marked price = 100 × 1.40 = 140. Selling price after 25% discount = 140 × 0.75 = 105. Profit = 105 − 100 = 5, i.e., 5% profit. (Using the successive formula directly: a = +40, b = −25. Net change = 40 − 25 + (40 × −25)/100 = 15 − 10 = 5%, confirming 5% profit.) Aspirants who simply subtract 40% − 25% = 15% and stop there, ignoring the cross-term, will incorrectly answer “15% profit,” which is not among the given options here precisely to flag that shortcut error.

B13. Answer: (c) 25% Price decreases by r = 20%. Required increase in consumption = r/(100−r) × 100 = 20/80 × 100 = 25%.

B14. Answer: (c) 88% Take total students = 100. Boys = 60, Girls = 40. Boys absent = 10% of 60 = 6 → Boys present = 54. Girls absent = 15% of 40 = 6 → Girls present = 34. Total present = 54 + 34 = 88, i.e., 88% of total students.

B15. Answer: (b) 0% (no change) Revenue = Price × Quantity sold. a = −20 (price), b = +25 (quantity/sales). Net % change = −20 + 25 + (−20 × 25)/100 = 5 − 5 = 0%. Total revenue is unchanged.

B16. Answer: (a) 1% decrease Combine the first two changes: a = +10, b = +20 → 10 + 20 + (10×20)/100 = 30 + 2 = 32%. Combine this +32% with the third change of −25%: 32 − 25 + (32×−25)/100 = 7 − 8 = −1%. (Direct check: 1.10 × 1.20 × 0.75 = 1.32 × 0.75 = 0.99, confirming a net 1% decrease.)

B17. Answer: (c) 10% 40,000 × (1 + r/100)² = 48,400 → (1 + r/100)² = 48,400/40,000 = 1.21 → (1 + r/100) = √1.21 = 1.1. So r = 10%.

B18. Answer: (c) ₹1,00,000 Original × (0.9)³ = 72,900 → Original × 0.729 = 72,900 → Original = 72,900/0.729 = ₹1,00,000.

B19. Answer: (b) 16% Let a = +25 (price). We need b such that 25 + b + (25b)/100 = 5 (the target net change). b(1.25) = 5 − 25 = −20 → b = −20/1.25 = −16%. So consumption must be reduced by 16%. (Check: 1.25 × 0.84 = 1.05, confirming a net +5% change.)

B20. Answer: (c) 21% Area = side × side, so a = b = 10. % error in area = 10 + 10 + (10×10)/100 = 20 + 1 = 21%.

B21. Answer: (c) 450 Let maximum marks = M, pass marks = P. From A: 0.42M = P − 12 → P = 0.42M + 12 From B: 0.50M = P + 24 → P = 0.50M − 24 Setting equal: 0.42M + 12 = 0.50M − 24 → 0.08M = 36 → M = 450.

B22. Answer: (b) 24,000 Winner’s margin as % of valid votes = 60% − 40% = 20% of valid votes = 4,080. Valid votes = 4,080 × (100/20) = 20,400. Since valid votes = 85% of total votes polled (15% being invalid): Total votes = 20,400/0.85 = 24,000.

B23. Answer: (c) ₹28,000 B’s income = 25,000 × (1 − 0.20) = 25,000 × 0.80 = ₹20,000. A’s income = 20,000 × 1.40 = ₹28,000.

B24. Answer: (b) ₹1,870 Price after discount = 2,000 × 0.85 = 1,700. Price after tax = 1,700 × 1.10 = ₹1,870.

B25. Answer: (c) 33,750 25,000 × 1.20 = 30,000 (end of year 1). 30,000 × 0.90 = 27,000 (end of year 2). 27,000 × 1.25 = 33,750 (end of year 3).

B26. Answer: (c) ₹1,65,000 For Machine X: Original × (0.80)² = 1,28,000 → Original × 0.64 = 1,28,000 → Original = ₹2,00,000. For Machine Y (same original price): 2,00,000 × 1.10 × 0.75 = 2,20,000 × 0.75 = ₹1,65,000.

B27. Answer: (b) 3.74% Combine length and breadth errors: a = +4, b = +5 → 4 + 5 + (4×5)/100 = 9 + 0.2 = 9.2%. Combine this 9.2% with the height’s −5% error: 9.2 − 5 + (9.2×−5)/100 = 4.2 − 0.46 = 3.74% (in excess).

B28. Answer: (c) 10% Let a = −10 (price). We need b such that −10 + b + (−10b)/100 = −1 (the target net change). b(1 − 0.10) = −1 + 10 = 9 → b × 0.90 = 9 → b = 10%. (Check: 0.90 × 1.10 = 0.99, confirming a net −1% change.)

B29. Answer: (c) 11,250 Valid votes = 30,000 × (1 − 0.10) = 30,000 × 0.90 = 27,000. Total ratio parts = 5 + 4 + 3 = 12. Winner’s votes = (5/12) × 27,000 = 11,250.

B30. Answer: (c) 40 Section A = (4/9) × 180 = 80. Section B = (5/9) × 180 = 100. Girls in A = 25% of 80 = 20. Girls in B = 20% of 100 = 20. Total girls = 20 + 20 = 40.