Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 549 · 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 ₹14, how much do 8 pens cost? (a) ₹20 (b) ₹112 (c) ₹56 (d) ₹63
2. 2.₹348 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹145 (b) ₹174 (c) ₹29 (d) ₹203
3. 3.If 4 kites cost ₹36, how much do 12 kites cost? (a) ₹432 (b) ₹108 (c) ₹117 (d) ₹44
4. 4.₹198 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹54 (b) ₹18 (c) ₹144 (d) ₹99
5. 5.If 8 notebooks cost ₹96, how much do 3 notebooks cost? (a) ₹91 (b) ₹48 (c) ₹36 (d) ₹288
6. 6.₹224 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹112 (b) ₹196 (c) ₹224 (d) ₹28
7. 7.9 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 19 days (b) 14 days (c) 6 days (d) 18 days
8. 8.If 6 pens cost ₹78, how much do 4 pens cost? (a) ₹52 (b) ₹312 (c) ₹76 (d) ₹65
9. 9.If 9 notebooks cost ₹198, how much do 10 notebooks cost? (a) ₹1980 (b) ₹242 (c) ₹199 (d) ₹220
10. 10.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 32 days (c) 33 days (d) 2 days
11. 11.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 7 days (c) 39 days (d) 40 days
12. 12.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 10 days (b) 13 days (c) 9 days (d) 8 days
13. 13.If 2 notebooks cost ₹6, how much do 10 notebooks cost? (a) ₹14 (b) ₹30 (c) ₹33 (d) ₹60
14. 14.If 5 pens cost ₹65, how much do 9 pens cost? (a) ₹117 (b) ₹585 (c) ₹69 (d) ₹130
15. 15.If 6 kites cost ₹126, how much do 11 kites cost? (a) ₹1386 (b) ₹131 (c) ₹231 (d) ₹252
16. 16.If 7 kites cost ₹175, how much do 6 kites cost? (a) ₹1050 (b) ₹150 (c) ₹175 (d) ₹174
17. 17.If 6 kites cost ₹30, how much do 4 kites cost? (a) ₹20 (b) ₹120 (c) ₹28 (d) ₹25
18. 18.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 18 days (d) 3 days
19. 19.If 3 notebooks cost ₹39, how much do 5 notebooks cost? (a) ₹195 (b) ₹78 (c) ₹41 (d) ₹65
20. 20.₹77 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹63 (b) ₹56 (c) ₹7 (d) ₹21
21. 21.If 2 notebooks cost ₹32, how much do 3 notebooks cost? (a) ₹96 (b) ₹64 (c) ₹33 (d) ₹48
22. 22.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 27 days (c) 28 days (d) 15 days
23. 23.₹288 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹144 (b) ₹32 (c) ₹128 (d) ₹160
24. 24.₹266 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹133 (b) ₹19 (c) ₹95 (d) ₹171
25. 25.If 3 kites cost ₹39, how much do 8 kites cost? (a) ₹312 (b) ₹104 (c) ₹44 (d) ₹117
26. 26.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 13 days (b) 4 days (c) 2 days (d) 3 days
27. 27.₹220 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹44 (b) ₹132 (c) ₹110 (d) ₹88
28. 28.If 3 notebooks cost ₹9, how much do 11 notebooks cost? (a) ₹33 (b) ₹99 (c) ₹36 (d) ₹17
29. 29.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 17 days (c) 16 days (d) 1 day
30. 30.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 11 days (d) 5 days
31. 31.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 21 days (c) 22 days (d) 3 days
32. 32.7 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) 19 days (d) 9 days
33. 33.₹87 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹59 (b) ₹58 (c) ₹87 (d) ₹29
34. 34.If 5 mangoes cost ₹90, how much do 6 mangoes cost? (a) ₹540 (b) ₹91 (c) ₹126 (d) ₹108
35. 35.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 6 days (c) 14 days (d) 24 days
36. 36.₹54 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹42 (b) ₹12 (c) ₹27 (d) ₹6
37. 37.₹440 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹320 (b) ₹120 (c) ₹220 (d) ₹40
38. 38.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 9 days (c) 15 days (d) 16 days
39. 39.3 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 16 days (c) 4 days (d) 11 days
40. 40.If 5 mangoes cost ₹25, how much do 10 mangoes cost? (a) ₹55 (b) ₹50 (c) ₹30 (d) ₹250

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