Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 127 · 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. 1.9 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 16 days (c) 15 days (d) 13 days
2. 2.If 6 mangoes cost ₹108, how much do 10 mangoes cost? (a) ₹1080 (b) ₹198 (c) ₹180 (d) ₹112
3. 3.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 7 days (d) 4 days
4. 4.7 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 22 days (d) 21 days
5. 5.If 6 pens cost ₹48, how much do 8 pens cost? (a) ₹384 (b) ₹50 (c) ₹72 (d) ₹64
6. 6.If 6 mangoes cost ₹24, how much do 7 mangoes cost? (a) ₹25 (b) ₹168 (c) ₹32 (d) ₹28
7. 7.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 5 days (d) 45 days
8. 8.If 3 pens cost ₹42, how much do 4 pens cost? (a) ₹43 (b) ₹56 (c) ₹168 (d) ₹70
9. 9.If 9 mangoes cost ₹162, how much do 4 mangoes cost? (a) ₹90 (b) ₹648 (c) ₹72 (d) ₹157
10. 10.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 9 days (d) 8 days
11. 11.₹56 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹14 (b) ₹28 (c) ₹56 (d) ₹42
12. 12.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 5 days (d) 6 days
13. 13.9 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 9 days (d) 10 days
14. 14.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 14 days (c) 7 days (d) 9 days
15. 15.If 2 kites cost ₹10, how much do 6 kites cost? (a) ₹60 (b) ₹14 (c) ₹35 (d) ₹30
16. 16.9 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) 40 days (d) 39 days
17. 17.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 2 days (d) 4 days
18. 18.₹336 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹42 (b) ₹294 (c) ₹168 (d) ₹336
19. 19.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 2 days (b) 18 days (c) 12 days (d) 3 days
20. 20.If 3 notebooks cost ₹9, how much do 7 notebooks cost? (a) ₹24 (b) ₹21 (c) ₹63 (d) ₹13
21. 21.If 4 pens cost ₹32, how much do 7 pens cost? (a) ₹64 (b) ₹224 (c) ₹56 (d) ₹35
22. 22.If 3 notebooks cost ₹51, how much do 6 notebooks cost? (a) ₹119 (b) ₹102 (c) ₹54 (d) ₹306
23. 23.If 9 kites cost ₹36, how much do 7 kites cost? (a) ₹32 (b) ₹34 (c) ₹252 (d) ₹28
24. 24.9 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 6 days (d) 1 day
25. 25.₹208 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹16 (b) ₹104 (c) ₹80 (d) ₹128
26. 26.₹91 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹13 (b) ₹26 (c) ₹65 (d) ₹78
27. 27.If 4 mangoes cost ₹16, how much do 8 mangoes cost? (a) ₹20 (b) ₹128 (c) ₹36 (d) ₹32
28. 28.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 13 days (c) 9 days (d) 23 days
29. 29.If 8 pens cost ₹88, how much do 3 pens cost? (a) ₹33 (b) ₹83 (c) ₹264 (d) ₹44
30. 30.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 11 days (c) 8 days (d) 10 days
31. 31.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 37 days (d) 36 days
32. 32.If 4 notebooks cost ₹76, how much do 12 notebooks cost? (a) ₹247 (b) ₹84 (c) ₹912 (d) ₹228
33. 33.₹290 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹29 (b) ₹145 (c) ₹87 (d) ₹203
34. 34.If 2 pens cost ₹42, how much do 3 pens cost? (a) ₹63 (b) ₹84 (c) ₹126 (d) ₹43
35. 35.If 7 pens cost ₹154, how much do 9 pens cost? (a) ₹156 (b) ₹220 (c) ₹198 (d) ₹1386
36. 36.If 3 pens cost ₹63, how much do 8 pens cost? (a) ₹504 (b) ₹68 (c) ₹189 (d) ₹168
37. 37.If 9 kites cost ₹45, how much do 10 kites cost? (a) ₹55 (b) ₹450 (c) ₹46 (d) ₹50
38. 38.₹476 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹34 (b) ₹170 (c) ₹306 (d) ₹238
39. 39.If 6 kites cost ₹138, how much do 5 kites cost? (a) ₹137 (b) ₹690 (c) ₹115 (d) ₹138
40. 40.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 39 days (c) 17 days (d) 40 days

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