Take sectional tests or a full 40-question mock on ratio, proportion, partnership, mixtures, alligation, and average with timers and answer review.
This route gives you four sectional sessions and a full-length mixed mock. Each question runs on a 60-second timer to train both concept clarity and test tempo.
Ratios, proportion, direct proportion, inverse proportion
Partnership and profit sharing
Mixtures, alligation, replacement
Average, weighted average, correction
1. Simplify the ratio 54:81.
Explanation: Divide both terms by their HCF, 27. So 54:81 = 2:3.
2. A sum of Rs 1260 is divided between Aarav and Meera in the ratio 2:5. Aarav gets:
Explanation: Total parts = 7. One part = 1260/7 = 180. Aarav gets 2 x 180 = Rs 360.
3. Two numbers are in the ratio 4:7 and their difference is 33. The smaller number is:
Explanation: Difference in ratio parts = 3. One part = 33/3 = 11. Smaller number = 4 x 11 = 44.
4. If x:y = 5:8 and y:z = 4:7, then x:y:z is:
Explanation: Make the common term y equal. Scale 4:7 to 8:14, so x:y:z = 5:8:14.
5. If a:b = c:d and a = 12, b = 18, c = 20, then d =
Explanation: Use a/b = c/d. So 12/18 = 20/d, hence d = (18 x 20) / 12 = 30.
6. A vehicle covers 150 km in 5 hours. At the same speed, it will cover 270 km in:
Explanation: Speed = 150/5 = 30 km/h. Time for 270 km = 270/30 = 9 h.
7. 16 workers can finish a job in 18 days. In how many days will 24 workers finish it?
Explanation: Workers and days are inversely proportional. 16 x 18 = 24 x d, so d = 12 days.
8. The fraction 63/84 expressed as a ratio in simplest form is:
Explanation: 63:84 reduces by 21 to 3:4.
9. A sum of Rs 1710 is divided between Aarav and Meera in the ratio 7:2. Aarav gets:
Explanation: Total parts = 9. One part = 1710/9 = 190. Aarav gets 7 x 190 = Rs 1330.
10. If a:b = c:d and a = 15, b = 25, c = 21, then d =
Explanation: 15/25 = 21/d, so d = (25 x 21) / 15 = 35.
11. Riya and Kabir invest Rs 32000 and Rs 48000 for the same time. Total profit is Rs 25000. Riya's share is:
Explanation: Profit ratio follows capital ratio 32000:48000 = 2:3. Riya gets 2/5 of 25000 = Rs 10000.
12. Ayaan invests Rs 22000 for 12 months and Meera invests Rs 18000 for 10 months. Their profit ratio is:
Explanation: Profit ratio = 22000 x 12 : 18000 x 10 = 264000:180000 = 22:15.
13. Neel starts a business with Rs 50000. After 6 months, Ishaan joins with Rs 30000. At year end, their profit ratio is:
Explanation: Neel: 50000 x 12 = 600000. Ishaan: 30000 x 6 = 180000. Ratio = 10:3.
14. Vani invests Rs 42000 at the start of the year. After 4 months, she changes it to Rs 54000. Kunal keeps Rs 36000 for 12 months. Their profit ratio is:
Explanation: Vani = 42000 x 4 + 54000 x 8 = 600000. Kunal = 36000 x 12 = 432000. Ratio = 25:18.
15. Aarav invests Rs 36000 for 12 months and Meera invests Rs 24000 for 9 months. Total profit is Rs 18000. Aarav's share is:
Explanation: Capital-months = 432000 and 216000. Aarav gets 432000/648000 of 18000 = Rs 12000.
16. Aarav invests Rs 20000 for 8 months and Meera invests Rs 30000 for 12 months. Total profit is Rs 15600. Meera's share is:
Explanation: Capital-months = 160000 and 360000. Meera gets 360000/520000 of 15600 = Rs 10800.
17. Ayaan invests Rs 45000 for 6 months and Meera invests Rs 30000 for 9 months. Their profit ratio is:
Explanation: 45000 x 6 = 270000 and 30000 x 9 = 270000, so the ratio is 1:1.
18. Neel starts a business with Rs 24000. After 2 months, Ishaan joins with Rs 48000. At year end, their profit ratio is:
Explanation: Neel = 24000 x 12 = 288000. Ishaan = 48000 x 10 = 480000. Ratio = 3:5.
19. Vani invests Rs 70000 at the start of the year. After 7 months, she changes it to Rs 35000. Kunal keeps Rs 50000 for 12 months. Their profit ratio is:
Explanation: Vani = 70000 x 7 + 35000 x 5 = 665000. Kunal = 50000 x 12 = 600000. Ratio = 133:120.
20. Riya and Kabir invest Rs 45000 and Rs 30000 for the same time. Total profit is Rs 21000. Riya's share is:
Explanation: Ratio = 45000:30000 = 3:2. Riya gets 3/5 of 21000 = Rs 12600.
21. Tea worth Rs 24/kg is mixed with tea worth Rs 40/kg to obtain a blend worth Rs 30/kg. The ratio of cheaper to dearer tea is:
Explanation: By alligation, cheaper:dearer = (40 - 30):(30 - 24) = 10:6.
22. How many litres of a 45% solution must be mixed with a 15% solution to make 20 L of a 30% solution?
Explanation: Alligation gives 15%:45% = 15:15, so both quantities are equal. Therefore the 45% solution is 10 L.
23. A container has 16 L of milk. 4 L is removed and replaced with water, and the process is repeated 2 times. Milk left is:
Explanation: Fraction left each time = 12/16. Milk left = 16 x (12/16)^2 = 9 L.
24. 6 kg of rice worth Rs 28/kg is mixed with 9 kg of rice worth Rs 40/kg. The mean price of the mixture is:
Explanation: Weighted mean = (28 x 6 + 40 x 9) / 15 = Rs 35.2/kg.
25. Tea worth Rs 50/kg is mixed with tea worth Rs 80/kg to obtain a blend worth Rs 62/kg. The ratio of cheaper to dearer tea is:
Explanation: By alligation, cheaper:dearer = (80 - 62):(62 - 50) = 18:12.
26. How many litres of a 36% solution must be mixed with a 12% solution to make 18 L of a 24% solution?
Explanation: Alligation gives 12%:36% = (36 - 24):(24 - 12) = 12:12, so both quantities are equal. Therefore the 36% solution is 9 L.
27. A container has 25 L of milk. 5 L is removed and replaced with water, and the process is repeated 2 times. Milk left is:
Explanation: Fraction left each time = 20/25. Milk left = 25 x (20/25)^2 = 16 L.
28. 11 kg of rice worth Rs 42/kg is mixed with 9 kg of rice worth Rs 56/kg. The mean price of the mixture is:
Explanation: Weighted mean = (42 x 11 + 56 x 9) / 20 = Rs 48.3/kg.
29. Tea worth Rs 32/kg is mixed with tea worth Rs 44/kg to obtain a blend worth Rs 38/kg. The ratio of cheaper to dearer tea is:
Explanation: By alligation, cheaper:dearer = (44 - 38):(38 - 32) = 6:6.
30. A container has 30 L of milk. 6 L is removed and replaced with water, and the process is repeated 3 times. Milk left is:
Explanation: Fraction left each time = 24/30 = 4/5. Milk left = 30 x (4/5)^3 = 15.36 L.
31. Find the average of 22, 28, 31, 35, 44.
Explanation: Average = (22 + 28 + 31 + 35 + 44) / 5 = 160/5 = 32.
32. The average of 7 numbers is 36. If the sum of 6 of them is 210, the missing number is:
Explanation: Total sum = 36 x 7 = 252. Missing number = 252 - 210 = 42.
33. The average marks of 25 students is 58, and of another 15 students is 70. The combined average is:
Explanation: Combined average = (25 x 58 + 15 x 70) / 40 = 62.5.
34. The average of 30 numbers was calculated as 52, but one number was taken as 64 instead of 94. The correct average is:
Explanation: Correction in total = 94 - 64 = 30. So average increases by 30/30 = 1. Correct average = 53.
35. A class has 20 boys with average score 64 and 30 girls with average score 70. The class average is:
Explanation: Weighted average = (20 x 64 + 30 x 70) / 50 = 67.6.
36. Find the average of 12, 16, 20, 24, 28, 32.
Explanation: Average = (12 + 16 + 20 + 24 + 28 + 32) / 6 = 132/6 = 22.
37. The average of 8 numbers is 33. If the sum of 7 of them is 231, the missing number is:
Explanation: Total sum = 33 x 8 = 264. Missing number = 264 - 231 = 33.
38. The average marks of 18 students is 47, and of another 22 students is 59. The combined average is:
Explanation: Combined average = (18 x 47 + 22 x 59) / 40 = 53.6.
39. The average of 50 numbers was calculated as 44, but one number was taken as 39 instead of 19. The correct average is:
Explanation: Correction in total = 19 - 39 = -20. So average changes by -20/50 = -0.4. Correct average = 43.6.
40. A class has 14 boys with average score 52 and 16 girls with average score 68. The class average is:
Explanation: Weighted average = (14 x 52 + 16 x 68) / 30 = 60.5333.
41. A total of Rs 3,600 is divided among A, B, and C in the ratio 2:3:4. How much more does C receive than A?
Explanation: Total parts = 9, so one part = $3600/9=400$. C gets 4 parts and A gets 2 parts. Difference = 2 parts = Rs 800.
42. A invests Rs 24,000 for 8 months and B invests Rs 18,000 for 12 months. If total profit is Rs 17,000, A's share is:
Explanation: Capital-months: A = $24000\times8=192000$, B = $18000\times12=216000$. Ratio = 8:9, so A's share $=\frac{8}{17}\times17000=8000$.
43. If 18 workers complete a job in 20 days, how many workers are needed to complete the same job in 12 days?
Explanation: Total work = $18\times20=360$ worker-days. Required workers $=360/12=30$.
44. The average weight of 12 students is 48 kg. A teacher weighing 72 kg joins them. What is the new average?
Explanation: Original total weight = $12\times48=576$ kg. New total = 576 + 72 = 648 kg. New average $=648/13=49.846$ kg.
45. The average of 25 numbers is 36. Later, one value recorded as 64 is corrected to 39. What is the corrected average?
Explanation: Total decreases by $64-39=25$. Average decreases by $25/25=1$, so corrected average = 35.