Q1. The average age of 14 employees in a department is A years. A new employee aged 59 joins, increasing the average age by 2 years. What is the new average age of the department?Correct Option C … Explanation: Total age of 14 employees = 14A. After the new employee joins, 15 employees have an average of (A + 2). So 14A + 59 = 15(A + 2) = 15A + 30, which gives A = 29. The new average = A + 2 = 31. Option B (29) is the old average, a common trap. Hence, option C.Q2. The number of players and non-players in a sports university are in the ratio 4:1. Out of the players, 66% play tennis, and 44% play badminton. If 60 players play both tennis and badminton, how many students are there in the university?Correct Option B … Explanation: Assuming every player plays at least one of the two games, players playing both = 66% + 44% − 100% = 10% of players. 10% of players = 60, so players = 600. Since players : non-players = 4 : 1, non-players = 150. Total students = 600 + 150 = 750. Option A (600) counts only the players. Hence, option B.Q3. Three friends, A, B, and C, played badminton against each other. Each pair played the same number of matches. No match ended in a tie. A won 60% of her matches against both B and C. B won twice as many matches against C as against A. If C won a total of 9 matches, how many matches did B win?Correct Option A … Explanation: Let each pair play n matches. A beats B in 0.6n matches, so B beats A in 0.4n. A beats C in 0.6n, so C beats A in 0.4n. B wins twice as many against C as against A: B beats C in 0.8n, so C beats B in 0.2n. C's total wins = 0.4n + 0.2n = 0.6n = 9, so n = 15. B's total wins = 0.4n + 0.8n = 1.2n = 18. Hence, option A.Q4. A, B, and C started a business. A invested twice as much as B, and B invested half of what C invested. C left the business at the end of 8 months, and A left after 6 months. If the total profit at the end of the year was Rs. 150,000, what is C's share of the profit?Correct Option D … Explanation: Let B = x. Then A = 2x and C = 2x. Capital × time: A = 2x × 6 = 12x, B = x × 12 = 12x, C = 2x × 8 = 16x. Profit ratio A : B : C = 12 : 12 : 16 = 3 : 3 : 4. C's share = (4/10) × 1,50,000 = Rs. 60,000. Hence, option D.Q5. 8 men can complete a task in 12 days, while 12 women can complete the same task in 16 days. If 4 men and 8 women work together for 5 days, what fraction of the total work remains to be completed?Correct Option C … Explanation: Total work = 8 × 12 = 96 man-days = 12 × 16 = 192 woman-days, so 1 man = 2 women. 4 men + 8 women = 8 + 8 = 16 women. In 5 days they do 16 × 5 = 80 woman-days = 80/192 = 5/12 of the work. Work remaining = 1 − 5/12 = 7/12. Option B (5/12) is the work completed, not the work remaining. Hence, option C.Q6. The difference between the compound interest and simple interest on a certain sum of money for 2 years, at an annual interest rate of 10%, is Rs. 800. What interest would be earned on the principal over 2 years if the interest were compounded half-yearly?Correct Option A … Explanation: For 2 years, CI − SI = P(r/100)². So 800 = P × (0.1)², which gives P = Rs. 80,000. Compounded half-yearly, the rate is 5% per half-year for 4 periods. Amount = 80,000 × (1.05)⁴ = 80,000 × 1.21550625 = Rs. 97,240.50. Interest = 97,240.50 − 80,000 = Rs. 17,240.50. Hence, option A.Q7. A person invests a total of Rs. 75,000 across two schemes offering simple interest at 6% and 9% per annum, respectively. If the total interest earned from both schemes after 3 years is Rs. 17,550, how much money was invested at 9%?Correct Option E … Explanation: Let the amount at 9% be x, so (75,000 − x) is at 6%. Interest over 3 years: 0.18(75,000 − x) + 0.27x = 17,550. This gives 13,500 + 0.09x = 17,550, so 0.09x = 4,050 and x = Rs. 45,000. Option A (Rs. 30,000) is the amount invested at 6%. Hence, option E.Q8. Meera drives from her home to the railway station to catch a train. She drives 40 km in the first hour, but realizes that she will be 45 minutes late if she continues at this speed. She increases her speed by 20 km/hr for the rest of the journey and arrives 15 minutes early. How many km is the station from her home?Correct Option C … Explanation: Let the remaining distance after the first hour be d km. Going from 45 minutes late to 15 minutes early saves 1 hour. So d/40 − d/60 = 1, which gives d/120 = 1 and d = 120 km. Total distance = 40 + 120 = 160 km. Option A-type traps come from forgetting to add the 40 km covered in the first hour. Hence, option C.Q9. A trader marks an article 60% above its cost price and offers a 15% discount on the marked price. He then pays a commission equal to 5% of the selling price to an intermediary. If the cost price of the article is ₹ 2800, what is the trader's net profit percentage?Correct Option A … Explanation: Marked price = 1.6 × 2,800 = ₹ 4,480. Selling price = 0.85 × 4,480 = ₹ 3,808. Commission = 5% of 3,808 = ₹ 190.40. Net receipt = 3,808 − 190.40 = ₹ 3,617.60. Net profit = 3,617.60 − 2,800 = ₹ 817.60. Profit % = 817.60/2,800 × 100 = 29.2%. Hence, option A.Q10. Three partners P, Q, and R invest in a business such that P's capital, if it earned simple interest at 10% per annum, would yield the same annual return as Q's capital invested at 8% per annum. If P invested Rs. 40,000 and the total capital invested by all three is Rs. 1,45,000, with R investing Rs. 55,000, find Q's share of an annual profit of Rs. 87,000.Correct Option E … Explanation: P's annual return at 10% = 0.10 × 40,000 = Rs. 4,000. Q's capital at 8% gives the same: 0.08 × Q = 4,000, so Q = Rs. 50,000. Check: 40,000 + 50,000 + 55,000 = 1,45,000. Profit ratio P : Q : R = 40 : 50 : 55 = 8 : 10 : 11. Q's share = (10/29) × 87,000 = Rs. 30,000. Hence, option E.Q11. A factory's monthly output grew by a certain fixed percentage every month for 3 consecutive months. If the output at the start was 8,000 units and after 3 months it became 10,648 units, what was the monthly growth rate?Correct Option C … Explanation: 8,000 × (1 + r)³ = 10,648, so (1 + r)³ = 10,648/8,000 = 1.331 = (1.1)³. Therefore 1 + r = 1.1 and r = 10%. Hence, option C.Q12. A retailer buys a batch of items at a certain price per unit. He sells 60% of the batch at a 25% profit and the remaining 40% at a 10% loss. If his overall profit on the entire batch is Rs. 3300, what was his total cost price for the batch?Correct Option B … Explanation: Let the total cost price be C. Profit on 60% of the batch = 0.25 × 0.6C = 0.15C. Loss on 40% of the batch = 0.10 × 0.4C = 0.04C. Net profit = 0.15C − 0.04C = 0.11C = 3,300, so C = Rs. 30,000. Hence, option B.Q13. A vessel contains a mixture of acid and water in the ratio 5:3. A second vessel contains the same two liquids in the ratio 2:3. In what ratio should quantities be taken from the two vessels to form a new mixture with acid and water in equal proportion?Correct Option D … Explanation: Acid fraction in vessel 1 = 5/8, in vessel 2 = 2/5, and in the target mixture = 1/2. By alligation, Vessel 1 : Vessel 2 = (1/2 − 2/5) : (5/8 − 1/2) = (1/10) : (1/8) = 8 : 10 = 4 : 5. Hence, option D.Q14. The average score of a class in a test is 72. The top 5 scorers, whose average score is 96, are excluded, which brings the class average down to 68. How many students were in the class originally?Correct Option E … Explanation: Let the original number of students be n. Total score = 72n. Removing the top 5 removes 5 × 96 = 480 marks. So 72n − 480 = 68(n − 5) = 68n − 340, which gives 4n = 140 and n = 35. Hence, option E.Q15. A sum of money invested at compound interest amounts to Rs. 26,620 at the end of the fourth year and Rs. 29,282 at the end of the sixth year. What was the original sum invested?Correct Option C … Explanation: Growth over 2 years (year 4 to year 6): (1 + r)² = 29,282/26,620 = 1.1. Growth over the first 4 years is therefore (1 + r)⁴ = (1.1)² = 1.21. Original sum = 26,620/1.21 = Rs. 22,000. The rate itself need not be found explicitly. Hence, option C.Q16. In an election, there were five candidates. 1/7th of the registered voters did not cast their votes, and 20% of the polled votes were declared invalid. One of the candidates received 30% of the valid votes, while the other four candidates received the remaining valid votes in the ratio 3:2:6:1. If the winner received 173 votes more than the candidate who secured the second-highest number of votes, then what was the number of polled votes?Correct Option B … Explanation: The remaining 70% of valid votes is split in the ratio 3 : 2 : 6 : 1 (total 12 parts), giving 17.5%, 11.67%, 35% and 5.83% of valid votes. The winner has 35% and the runner-up has 30%. Difference = 5% of valid votes = 173, so valid votes = 3,460. Valid votes are 80% of polled votes, so polled votes = 3,460/0.8 = 4,325. Option A (3,460) is the number of valid votes, not polled votes. Hence, option B.Q17. The daily earnings of three workers, A, B, and C, are constant. The total earnings of A and B together in 4 days are equal to C’s earnings in 11 days. The total earnings of A and C together in 5 days are equal to B’s earnings in 7 days. What is the ratio of the daily earnings of the highest-earning worker to those of the lowest-earning worker?Correct Option A … Explanation: 4(A + B) = 11C gives A + B = 11C/4. 5(A + C) = 7B gives A = (7B − 5C)/5. Substituting: (7B − 5C)/5 + B = 11C/4, so (12B − 5C)/5 = 11C/4. This simplifies to 48B = 75C, so B = 25C/16. Then A = 11C/4 − 25C/16 = 19C/16. So A : B : C = 19 : 25 : 16. Highest (B) : Lowest (C) = 25 : 16. Hence, option A.Q18. At their usual efficiency levels, Ankita and Bikas can complete a task together in 21 days. After working together at their usual efficiencies for 9 days, Ankita started working at half of her usual efficiency, while Bikas started working at three times his usual efficiency. The task was completed in 9 more days. How many days would Ankita take to complete the task alone at her usual efficiency?Correct Option D … Explanation: Let Ankita's and Bikas's daily work be a and b, with a + b = 1/21. In the first 9 days they complete 9/21 = 3/7 of the task, leaving 4/7. In the next 9 days: 9(a/2 + 3b) = 4/7, so a/2 + 3b = 4/63. Substituting b = 3/63 − a: a/2 + 9/63 − 3a = 4/63, so 2.5a = 5/63 and a = 2/63. Ankita alone takes 63/2 = 31.5 days. Hence, option D.Q19. A vessel is full of 60 liters of pure milk. First, 6 liters of milk is taken out and replaced with water. Then, 12 liters of the new mixture is taken out and replaced with water. Finally, 18 liters of the resulting mixture is taken out and replaced with water. What is the final quantity of milk in the vessel?Correct Option E … Explanation: Each replacement keeps the fraction (60 − removed)/60 of the milk. Final milk = 60 × (54/60) × (48/60) × (42/60) = 60 × 0.9 × 0.8 × 0.7 = 30.24 liters. Hence, option E.Q20. The cost of 2 notebooks, 3 pens, and 4 erasers is Rs. 64. The unit costs of a notebook, a pen, and an eraser are in the ratio 3:2:1. What is the total cost of 5 notebooks, 2 pens, and 6 erasers?Correct Option D … Explanation: Let the unit costs be 3k, 2k and k. Then 2(3k) + 3(2k) + 4(k) = 16k = 64, so k = 4. Notebook = Rs. 12, pen = Rs. 8, eraser = Rs. 4. Required cost = 5(12) + 2(8) + 6(4) = 60 + 16 + 24 = Rs. 100. Hence, option D.
