Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 8 · 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. 1.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 7 days (c) 11 days (d) 16 days
2. 2.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 8 days (d) 9 days
3. 3.₹392 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹252 (b) ₹140 (c) ₹196 (d) ₹28
4. 4.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 7 days (d) 3 days
5. 5.₹230 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹23 (b) ₹207 (c) ₹230 (d) ₹115
6. 6.If 5 notebooks cost ₹70, how much do 10 notebooks cost? (a) ₹700 (b) ₹154 (c) ₹140 (d) ₹75
7. 7.₹153 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹153 (b) ₹137 (c) ₹136 (d) ₹17
8. 8.If 5 mangoes cost ₹110, how much do 6 mangoes cost? (a) ₹660 (b) ₹132 (c) ₹111 (d) ₹154
9. 9.If 5 kites cost ₹110, how much do 6 kites cost? (a) ₹111 (b) ₹660 (c) ₹154 (d) ₹132
10. 10.₹210 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹105 (b) ₹75 (c) ₹135 (d) ₹15
11. 11.If 4 kites cost ₹28, how much do 3 kites cost? (a) ₹84 (b) ₹27 (c) ₹21 (d) ₹28
12. 12.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 8 days (d) 5 days
13. 13.If 3 pens cost ₹48, how much do 8 pens cost? (a) ₹128 (b) ₹384 (c) ₹53 (d) ₹144
14. 14.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 15 days (c) 14 days (d) 12 days
15. 15.If 3 pens cost ₹57, how much do 2 pens cost? (a) ₹56 (b) ₹114 (c) ₹38 (d) ₹57
16. 16.If 2 pens cost ₹42, how much do 6 pens cost? (a) ₹147 (b) ₹126 (c) ₹252 (d) ₹46
17. 17.If 4 notebooks cost ₹24, how much do 5 notebooks cost? (a) ₹30 (b) ₹36 (c) ₹120 (d) ₹25
18. 18.If 8 notebooks cost ₹192, how much do 6 notebooks cost? (a) ₹190 (b) ₹144 (c) ₹168 (d) ₹1152
19. 19.If 3 pens cost ₹48, how much do 10 pens cost? (a) ₹55 (b) ₹480 (c) ₹176 (d) ₹160
20. 20.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 1 day (d) 8 days
21. 21.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 17 days (d) 25 days
22. 22.6 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 12 days (c) 8 days (d) 16 days
23. 23.If 2 kites cost ₹36, how much do 4 kites cost? (a) ₹38 (b) ₹90 (c) ₹72 (d) ₹144
24. 24.If 5 notebooks cost ₹75, how much do 12 notebooks cost? (a) ₹195 (b) ₹900 (c) ₹180 (d) ₹82
25. 25.₹300 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹300 (b) ₹250 (c) ₹150 (d) ₹50
26. 26.If 3 kites cost ₹36, how much do 4 kites cost? (a) ₹37 (b) ₹60 (c) ₹48 (d) ₹144
27. 27.₹99 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹81 (b) ₹90 (c) ₹18 (d) ₹9
28. 28.₹352 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹44 (b) ₹176 (c) ₹308 (d) ₹352
29. 29.₹330 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹270 (b) ₹60 (c) ₹165 (d) ₹30
30. 30.If 9 pens cost ₹126, how much do 7 pens cost? (a) ₹882 (b) ₹98 (c) ₹112 (d) ₹124
31. 31.If 7 pens cost ₹175, how much do 4 pens cost? (a) ₹100 (b) ₹172 (c) ₹700 (d) ₹125
32. 32.If 5 notebooks cost ₹40, how much do 10 notebooks cost? (a) ₹45 (b) ₹88 (c) ₹400 (d) ₹80
33. 33.If 2 mangoes cost ₹34, how much do 5 mangoes cost? (a) ₹37 (b) ₹170 (c) ₹102 (d) ₹85
34. 34.If 6 mangoes cost ₹78, how much do 11 mangoes cost? (a) ₹156 (b) ₹143 (c) ₹83 (d) ₹858
35. 35.₹171 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹19 (b) ₹133 (c) ₹38 (d) ₹152
36. 36.If 2 mangoes cost ₹50, how much do 5 mangoes cost? (a) ₹250 (b) ₹53 (c) ₹150 (d) ₹125
37. 37.If 2 pens cost ₹40, how much do 11 pens cost? (a) ₹220 (b) ₹440 (c) ₹49 (d) ₹240
38. 38.₹100 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹40 (b) ₹60 (c) ₹50 (d) ₹20
39. 39.₹88 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹44 (b) ₹55 (c) ₹11 (d) ₹33
40. 40.5 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 11 days (d) 9 days

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