Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 983 · 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. 1.6 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 12 days (d) 3 days
2. 2.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 8 days (d) 2 days
3. 3.₹144 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹16 (b) ₹72 (c) ₹144 (d) ₹128
4. 4.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 19 days (c) 12 days (d) 18 days
5. 5.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 13 days (c) 5 days (d) 4 days
6. 6.If 9 notebooks cost ₹225, how much do 10 notebooks cost? (a) ₹275 (b) ₹250 (c) ₹226 (d) ₹2250
7. 7.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 15 days (d) 14 days
8. 8.If 8 notebooks cost ₹56, how much do 4 notebooks cost? (a) ₹52 (b) ₹28 (c) ₹224 (d) ₹35
9. 9.₹473 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹215 (b) ₹301 (c) ₹258 (d) ₹43
10. 10.If 3 pens cost ₹60, how much do 9 pens cost? (a) ₹180 (b) ₹66 (c) ₹200 (d) ₹540
11. 11.₹490 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹35 (b) ₹315 (c) ₹175 (d) ₹245
12. 12.If 5 notebooks cost ₹20, how much do 6 notebooks cost? (a) ₹24 (b) ₹28 (c) ₹21 (d) ₹120
13. 13.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 32 days (b) 33 days (c) 14 days (d) 2 days
14. 14.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 27 days (c) 13 days (d) 5 days
15. 15.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 7 days (d) 8 days
16. 16.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 40 days (b) 41 days (c) 16 days (d) 4 days
17. 17.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 5 days (d) 17 days
18. 18.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 14 days (d) 20 days
19. 19.If 6 notebooks cost ₹102, how much do 5 notebooks cost? (a) ₹85 (b) ₹102 (c) ₹101 (d) ₹510
20. 20.If 2 notebooks cost ₹20, how much do 7 notebooks cost? (a) ₹25 (b) ₹70 (c) ₹140 (d) ₹80
21. 21.If 2 kites cost ₹44, how much do 4 kites cost? (a) ₹176 (b) ₹46 (c) ₹88 (d) ₹110
22. 22.If 9 mangoes cost ₹81, how much do 4 mangoes cost? (a) ₹45 (b) ₹76 (c) ₹324 (d) ₹36
23. 23.If 6 pens cost ₹96, how much do 11 pens cost? (a) ₹1056 (b) ₹192 (c) ₹176 (d) ₹101
24. 24.₹76 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹76 (b) ₹38 (c) ₹19 (d) ₹57
25. 25.₹261 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹145 (b) ₹116 (c) ₹174 (d) ₹29
26. 26.If 3 mangoes cost ₹54, how much do 2 mangoes cost? (a) ₹54 (b) ₹36 (c) ₹53 (d) ₹108
27. 27.₹189 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹108 (b) ₹27 (c) ₹135 (d) ₹81
28. 28.₹245 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹35 (b) ₹211 (c) ₹245 (d) ₹210
29. 29.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 15 days (d) 8 days
30. 30.₹576 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹336 (b) ₹240 (c) ₹48 (d) ₹288
31. 31.If 9 pens cost ₹72, how much do 4 pens cost? (a) ₹40 (b) ₹32 (c) ₹67 (d) ₹288
32. 32.3 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) 3 days (d) 2 days
33. 33.₹330 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹60 (b) ₹30 (c) ₹270 (d) ₹165
34. 34.₹208 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹26 (b) ₹104 (c) ₹130 (d) ₹78
35. 35.₹528 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹44 (b) ₹220 (c) ₹264 (d) ₹308
36. 36.If 4 notebooks cost ₹12, how much do 5 notebooks cost? (a) ₹15 (b) ₹18 (c) ₹13 (d) ₹60
37. 37.If 4 pens cost ₹80, how much do 9 pens cost? (a) ₹85 (b) ₹180 (c) ₹720 (d) ₹200
38. 38.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 26 days (d) 11 days
39. 39.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 35 days (b) 36 days (c) 19 days (d) 11 days
40. 40.If 8 notebooks cost ₹80, how much do 6 notebooks cost? (a) ₹70 (b) ₹78 (c) ₹60 (d) ₹480

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