Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 433 · 40 questions

How to solve it (Go through one): Unitary: cost of one = total ÷ number; then multiply by how many you need. Ratio p : q of a total: one part = total ÷ (p + q); a share = its parts × one part. Workers and days go the opposite way: total work = workers × days; days = total work ÷ new number of workers.

1. 1.₹637 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹392 (b) ₹441 (c) ₹245 (d) ₹49
2. 2.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 5 days (d) 2 days
3. 3.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 18 days (b) 14 days (c) 3 days (d) 2 days
4. 4.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 8 days (d) 9 days
5. 5.If 8 mangoes cost ₹192, how much do 2 mangoes cost? (a) ₹48 (b) ₹384 (c) ₹72 (d) ₹186
6. 6.₹48 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹6 (b) ₹24 (c) ₹42 (d) ₹48
7. 7.If 5 pens cost ₹55, how much do 11 pens cost? (a) ₹605 (b) ₹121 (c) ₹61 (d) ₹132
8. 8.₹624 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹384 (b) ₹312 (c) ₹240 (d) ₹48
9. 9.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 2 days (d) 9 days
10. 10.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 20 days (b) 21 days (c) 14 days (d) 16 days
11. 11.₹252 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹252 (b) ₹224 (c) ₹28 (d) ₹126
12. 12.₹171 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹38 (b) ₹19 (c) ₹152 (d) ₹133
13. 13.If 2 mangoes cost ₹36, how much do 10 mangoes cost? (a) ₹180 (b) ₹198 (c) ₹44 (d) ₹360
14. 14.₹55 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹22 (b) ₹11 (c) ₹44 (d) ₹33
15. 15.₹256 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹32 (b) ₹160 (c) ₹96 (d) ₹128
16. 16.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 2 days (d) 3 days
17. 17.₹154 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹77 (b) ₹132 (c) ₹154 (d) ₹22
18. 18.₹253 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹138 (b) ₹161 (c) ₹115 (d) ₹23
19. 19.If 3 notebooks cost ₹66, how much do 5 notebooks cost? (a) ₹68 (b) ₹132 (c) ₹110 (d) ₹330
20. 20.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 22 days (c) 13 days (d) 9 days
21. 21.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 11 days (d) 2 days
22. 22.₹243 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹162 (b) ₹135 (c) ₹27 (d) ₹108
23. 23.₹240 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹90 (b) ₹150 (c) ₹120 (d) ₹30
24. 24.If 8 kites cost ₹128, how much do 7 kites cost? (a) ₹896 (b) ₹112 (c) ₹128 (d) ₹127
25. 25.₹330 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹33 (b) ₹330 (c) ₹297 (d) ₹165
26. 26.₹117 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹45 (b) ₹81 (c) ₹72 (d) ₹9
27. 27.₹55 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹40 (b) ₹5 (c) ₹15 (d) ₹45
28. 28.₹481 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹148 (b) ₹333 (c) ₹37 (d) ₹370
29. 29.If 8 mangoes cost ₹144, how much do 12 mangoes cost? (a) ₹234 (b) ₹148 (c) ₹1728 (d) ₹216
30. 30.If 8 pens cost ₹136, how much do 7 pens cost? (a) ₹136 (b) ₹135 (c) ₹952 (d) ₹119
31. 31.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 9 days (d) 1 day
32. 32.₹55 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹10 (b) ₹45 (c) ₹5 (d) ₹50
33. 33.₹209 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹152 (b) ₹19 (c) ₹133 (d) ₹76
34. 34.If 4 notebooks cost ₹96, how much do 11 notebooks cost? (a) ₹264 (b) ₹288 (c) ₹103 (d) ₹1056
35. 35.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 14 days (c) 15 days (d) 10 days
36. 36.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 10 days (c) 3 days (d) 5 days
37. 37.If 4 pens cost ₹20, how much do 5 pens cost? (a) ₹30 (b) ₹25 (c) ₹100 (d) ₹21
38. 38.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 11 days (c) 9 days (d) 17 days
39. 39.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 6 days (c) 8 days (d) 7 days
40. 40.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 6 days (d) 17 days

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