Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 828 · 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.If 2 pens cost ₹6, how much do 4 pens cost? (a) ₹15 (b) ₹12 (c) ₹24 (d) ₹8
2. 2.If 7 notebooks cost ₹56, how much do 10 notebooks cost? (a) ₹88 (b) ₹59 (c) ₹560 (d) ₹80
3. 3.₹90 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹10 (b) ₹20 (c) ₹45 (d) ₹70
4. 4.₹297 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹189 (b) ₹162 (c) ₹27 (d) ₹135
5. 5.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 2 days (c) 10 days (d) 3 days
6. 6.₹45 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹36 (b) ₹27 (c) ₹9 (d) ₹18
7. 7.₹275 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹200 (b) ₹25 (c) ₹225 (d) ₹75
8. 8.₹126 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹63 (b) ₹18 (c) ₹54 (d) ₹72
9. 9.If 6 mangoes cost ₹114, how much do 3 mangoes cost? (a) ₹342 (b) ₹111 (c) ₹76 (d) ₹57
10. 10.If 2 mangoes cost ₹12, how much do 8 mangoes cost? (a) ₹54 (b) ₹18 (c) ₹96 (d) ₹48
11. 11.If 6 notebooks cost ₹84, how much do 2 notebooks cost? (a) ₹80 (b) ₹42 (c) ₹168 (d) ₹28
12. 12.If 2 notebooks cost ₹50, how much do 12 notebooks cost? (a) ₹600 (b) ₹60 (c) ₹300 (d) ₹325
13. 13.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 10 days (d) 12 days
14. 14.If 8 pens cost ₹144, how much do 3 pens cost? (a) ₹432 (b) ₹72 (c) ₹139 (d) ₹54
15. 15.If 5 pens cost ₹105, how much do 3 pens cost? (a) ₹63 (b) ₹84 (c) ₹103 (d) ₹315
16. 16.If 8 kites cost ₹192, how much do 3 kites cost? (a) ₹96 (b) ₹187 (c) ₹576 (d) ₹72
17. 17.₹261 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹29 (b) ₹145 (c) ₹116 (d) ₹174
18. 18.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 15 days (c) 6 days (d) 7 days
19. 19.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 5 days (c) 4 days (d) 6 days
20. 20.If 7 notebooks cost ₹77, how much do 6 notebooks cost? (a) ₹462 (b) ₹66 (c) ₹76 (d) ₹77
21. 21.₹207 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹92 (b) ₹23 (c) ₹138 (d) ₹115
22. 22.3 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
23. 23.If 3 mangoes cost ₹66, how much do 9 mangoes cost? (a) ₹72 (b) ₹198 (c) ₹220 (d) ₹594
24. 24.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 15 days (c) 13 days (d) 21 days
25. 25.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 21 days (b) 5 days (c) 9 days (d) 45 days
26. 26.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 28 days (c) 16 days (d) 7 days
27. 27.If 9 notebooks cost ₹198, how much do 6 notebooks cost? (a) ₹1188 (b) ₹195 (c) ₹154 (d) ₹132
28. 28.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 4 days (c) 10 days (d) 15 days
29. 29.If 3 pens cost ₹12, how much do 5 pens cost? (a) ₹60 (b) ₹14 (c) ₹20 (d) ₹24
30. 30.4 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) 18 days (d) 3 days
31. 31.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 16 days (d) 17 days
32. 32.₹442 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹136 (b) ₹34 (c) ₹221 (d) ₹306
33. 33.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 3 days (d) 5 days
34. 34.If 9 pens cost ₹36, how much do 11 pens cost? (a) ₹396 (b) ₹44 (c) ₹38 (d) ₹48
35. 35.₹65 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹20 (b) ₹45 (c) ₹5 (d) ₹50
36. 36.If 8 notebooks cost ₹64, how much do 11 notebooks cost? (a) ₹96 (b) ₹88 (c) ₹67 (d) ₹704
37. 37.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 49 days (b) 4 days (c) 9 days (d) 19 days
38. 38.₹154 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹84 (b) ₹77 (c) ₹70 (d) ₹14
39. 39.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 19 days (d) 18 days
40. 40.If 4 pens cost ₹28, how much do 3 pens cost? (a) ₹27 (b) ₹21 (c) ₹84 (d) ₹28

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