Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 656 · 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 ₹38, how much do 10 pens cost? (a) ₹209 (b) ₹380 (c) ₹190 (d) ₹46
2. 2.₹156 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹12 (b) ₹78 (c) ₹108 (d) ₹48
3. 3.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 8 days (d) 2 days
4. 4.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 16 days (d) 11 days
5. 5.8 workers can build a wall in 15 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 30 days (c) 19 days (d) 31 days
6. 6.₹546 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹168 (b) ₹42 (c) ₹378 (d) ₹273
7. 7.If 4 kites cost ₹40, how much do 5 kites cost? (a) ₹50 (b) ₹41 (c) ₹200 (d) ₹60
8. 8.₹190 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹19 (b) ₹57 (c) ₹95 (d) ₹133
9. 9.₹132 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹12 (b) ₹66 (c) ₹60 (d) ₹72
10. 10.If 6 notebooks cost ₹114, how much do 10 notebooks cost? (a) ₹118 (b) ₹190 (c) ₹209 (d) ₹1140
11. 11.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 9 days (d) 5 days
12. 12.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 10 days (c) 8 days (d) 11 days
13. 13.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 3 days (d) 7 days
14. 14.₹66 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹6 (b) ₹33 (c) ₹36 (d) ₹30
15. 15.6 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 18 days (d) 24 days
16. 16.If 4 pens cost ₹76, how much do 9 pens cost? (a) ₹81 (b) ₹190 (c) ₹684 (d) ₹171
17. 17.If 9 mangoes cost ₹135, how much do 12 mangoes cost? (a) ₹195 (b) ₹1620 (c) ₹138 (d) ₹180
18. 18.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 14 days (c) 11 days (d) 16 days
19. 19.If 8 pens cost ₹168, how much do 2 pens cost? (a) ₹42 (b) ₹336 (c) ₹63 (d) ₹162
20. 20.₹152 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹76 (b) ₹38 (c) ₹152 (d) ₹114
21. 21.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 20 days (c) 11 days (d) 5 days
22. 22.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 15 days (c) 9 days (d) 14 days
23. 23.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 27 days (c) 3 days (d) 15 days
24. 24.₹462 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹231 (b) ₹165 (c) ₹33 (d) ₹297
25. 25.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 24 days (b) 8 days (c) 6 days (d) 16 days
26. 26.₹42 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹35 (b) ₹42 (c) ₹7 (d) ₹21
27. 27.If 9 kites cost ₹198, how much do 4 kites cost? (a) ₹110 (b) ₹193 (c) ₹88 (d) ₹792
28. 28.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 15 days (d) 6 days
29. 29.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 12 days (c) 9 days (d) 8 days
30. 30.₹105 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹15 (b) ₹75 (c) ₹60 (d) ₹45
31. 31.If 5 notebooks cost ₹20, how much do 4 notebooks cost? (a) ₹19 (b) ₹20 (c) ₹80 (d) ₹16
32. 32.If 3 kites cost ₹36, how much do 10 kites cost? (a) ₹43 (b) ₹132 (c) ₹360 (d) ₹120
33. 33.₹66 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹54 (b) ₹33 (c) ₹12 (d) ₹6
34. 34.₹84 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹42 (b) ₹12 (c) ₹84 (d) ₹72
35. 35.If 3 notebooks cost ₹27, how much do 4 notebooks cost? (a) ₹45 (b) ₹108 (c) ₹36 (d) ₹28
36. 36.₹377 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹261 (b) ₹116 (c) ₹29 (d) ₹290
37. 37.₹385 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹210 (b) ₹245 (c) ₹175 (d) ₹35
38. 38.₹144 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹144 (b) ₹128 (c) ₹72 (d) ₹16
39. 39.If 6 notebooks cost ₹24, how much do 4 notebooks cost? (a) ₹16 (b) ₹96 (c) ₹20 (d) ₹22
40. 40.If 6 kites cost ₹48, how much do 12 kites cost? (a) ₹576 (b) ₹54 (c) ₹96 (d) ₹104

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