Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 982 · 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. 1.4 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 23 days (b) 45 days (c) 7 days (d) 5 days
2. 2.₹160 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹80 (b) ₹60 (c) ₹100 (d) ₹20
3. 3.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 6 days (c) 10 days (d) 4 days
4. 4.₹100 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹30 (b) ₹70 (c) ₹10 (d) ₹50
5. 5.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 19 days (c) 4 days (d) 49 days
6. 6.₹207 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹184 (b) ₹161 (c) ₹23 (d) ₹46
7. 7.₹297 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹243 (b) ₹81 (c) ₹216 (d) ₹27
8. 8.If 4 pens cost ₹80, how much do 11 pens cost? (a) ₹880 (b) ₹220 (c) ₹87 (d) ₹240
9. 9.₹126 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹84 (b) ₹126 (c) ₹42 (d) ₹63
10. 10.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 1 day (d) 8 days
11. 11.If 4 kites cost ₹24, how much do 9 kites cost? (a) ₹54 (b) ₹60 (c) ₹29 (d) ₹216
12. 12.₹99 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹81 (b) ₹9 (c) ₹72 (d) ₹27
13. 13.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 56 days (c) 20 days (d) 57 days
14. 14.If 2 notebooks cost ₹24, how much do 4 notebooks cost? (a) ₹26 (b) ₹96 (c) ₹48 (d) ₹60
15. 15.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 6 days (d) 4 days
16. 16.If 5 mangoes cost ₹40, how much do 2 mangoes cost? (a) ₹80 (b) ₹24 (c) ₹16 (d) ₹37
17. 17.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 9 days (d) 4 days
18. 18.₹506 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹322 (b) ₹184 (c) ₹46 (d) ₹253
19. 19.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 22 days (c) 23 days (d) 14 days
20. 20.₹165 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹105 (b) ₹15 (c) ₹120 (d) ₹60
21. 21.₹198 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹22 (b) ₹99 (c) ₹154 (d) ₹44
22. 22.If 6 kites cost ₹18, how much do 7 kites cost? (a) ₹19 (b) ₹21 (c) ₹24 (d) ₹126
23. 23.If 9 notebooks cost ₹81, how much do 10 notebooks cost? (a) ₹99 (b) ₹82 (c) ₹810 (d) ₹90
24. 24.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 4 days (d) 3 days
25. 25.If 6 pens cost ₹48, how much do 3 pens cost? (a) ₹144 (b) ₹45 (c) ₹32 (d) ₹24
26. 26.If 5 pens cost ₹45, how much do 2 pens cost? (a) ₹27 (b) ₹42 (c) ₹90 (d) ₹18
27. 27.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 19 days (d) 2 days
28. 28.₹126 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹70 (b) ₹56 (c) ₹14 (d) ₹63
29. 29.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 25 days (c) 12 days (d) 24 days
30. 30.₹329 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹282 (b) ₹47 (c) ₹329 (d) ₹283
31. 31.₹320 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹32 (b) ₹160 (c) ₹288 (d) ₹320
32. 32.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 40 days (c) 39 days (d) 9 days
33. 33.6 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 9 days (d) 25 days
34. 34.₹387 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹301 (b) ₹344 (c) ₹86 (d) ₹43
35. 35.If 8 kites cost ₹128, how much do 2 kites cost? (a) ₹256 (b) ₹48 (c) ₹32 (d) ₹122
36. 36.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 19 days (c) 39 days (d) 40 days
37. 37.If 7 notebooks cost ₹147, how much do 11 notebooks cost? (a) ₹252 (b) ₹231 (c) ₹151 (d) ₹1617
38. 38.₹78 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹78 (b) ₹65 (c) ₹39 (d) ₹13
39. 39.₹322 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹161 (b) ₹207 (c) ₹23 (d) ₹115
40. 40.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 9 days (d) 8 days

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