Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 500 · 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 4 pens cost ₹28, how much do 10 pens cost? (a) ₹280 (b) ₹34 (c) ₹70 (d) ₹77
2. 2.If 5 notebooks cost ₹50, how much do 10 notebooks cost? (a) ₹500 (b) ₹55 (c) ₹110 (d) ₹100
3. 3.If 3 mangoes cost ₹66, how much do 12 mangoes cost? (a) ₹264 (b) ₹286 (c) ₹75 (d) ₹792
4. 4.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 18 days (c) 2 days (d) 19 days
5. 5.If 7 kites cost ₹56, how much do 10 kites cost? (a) ₹88 (b) ₹560 (c) ₹59 (d) ₹80
6. 6.₹144 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹120 (b) ₹72 (c) ₹144 (d) ₹24
7. 7.If 7 pens cost ₹133, how much do 12 pens cost? (a) ₹138 (b) ₹247 (c) ₹228 (d) ₹1596
8. 8.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 17 days (d) 4 days
9. 9.₹333 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹296 (b) ₹37 (c) ₹333 (d) ₹297
10. 10.₹518 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹37 (b) ₹259 (c) ₹333 (d) ₹185
11. 11.If 8 kites cost ₹176, how much do 9 kites cost? (a) ₹198 (b) ₹220 (c) ₹177 (d) ₹1584
12. 12.If 9 mangoes cost ₹126, how much do 3 mangoes cost? (a) ₹378 (b) ₹120 (c) ₹56 (d) ₹42
13. 13.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 26 days (d) 27 days
14. 14.6 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 16 days (c) 22 days (d) 21 days
15. 15.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 21 days (d) 45 days
16. 16.₹110 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹10 (b) ₹20 (c) ₹90 (d) ₹55
17. 17.₹320 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹96 (b) ₹32 (c) ₹160 (d) ₹224
18. 18.If 9 notebooks cost ₹117, how much do 5 notebooks cost? (a) ₹113 (b) ₹585 (c) ₹78 (d) ₹65
19. 19.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 3 days (d) 4 days
20. 20.₹161 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹46 (b) ₹115 (c) ₹138 (d) ₹23
21. 21.₹108 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹63 (b) ₹9 (c) ₹54 (d) ₹45
22. 22.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 12 days (d) 17 days
23. 23.₹174 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹145 (b) ₹29 (c) ₹174 (d) ₹87
24. 24.If 3 notebooks cost ₹30, how much do 2 notebooks cost? (a) ₹29 (b) ₹20 (c) ₹60 (d) ₹30
25. 25.If 5 pens cost ₹70, how much do 2 pens cost? (a) ₹140 (b) ₹67 (c) ₹28 (d) ₹42
26. 26.₹270 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹27 (b) ₹189 (c) ₹135 (d) ₹81
27. 27.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 28 days (d) 7 days
28. 28.5 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 19 days (b) 5 days (c) 4 days (d) 6 days
29. 29.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 9 days (d) 13 days
30. 30.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹60 (b) ₹108 (c) ₹84 (d) ₹12
31. 31.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 44 days (b) 5 days (c) 17 days (d) 45 days
32. 32.9 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 5 days (c) 55 days (d) 54 days
33. 33.₹312 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹156 (b) ₹24 (c) ₹96 (d) ₹216
34. 34.If 2 notebooks cost ₹8, how much do 8 notebooks cost? (a) ₹64 (b) ₹32 (c) ₹36 (d) ₹14
35. 35.If 8 notebooks cost ₹24, how much do 3 notebooks cost? (a) ₹19 (b) ₹9 (c) ₹12 (d) ₹72
36. 36.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 28 days (d) 3 days
37. 37.If 9 pens cost ₹225, how much do 12 pens cost? (a) ₹300 (b) ₹325 (c) ₹228 (d) ₹2700
38. 38.₹68 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹34 (b) ₹68 (c) ₹51 (d) ₹17
39. 39.₹77 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹7 (b) ₹56 (c) ₹63 (d) ₹21
40. 40.If 8 notebooks cost ₹136, how much do 7 notebooks cost? (a) ₹135 (b) ₹136 (c) ₹952 (d) ₹119

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