Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 220 · 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. 1.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 15 days (d) 14 days
2. 2.₹432 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹48 (b) ₹240 (c) ₹192 (d) ₹216
3. 3.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 37 days (c) 36 days (d) 15 days
4. 4.If 7 mangoes cost ₹98, how much do 10 mangoes cost? (a) ₹154 (b) ₹140 (c) ₹980 (d) ₹101
5. 5.If 3 kites cost ₹27, how much do 4 kites cost? (a) ₹36 (b) ₹45 (c) ₹108 (d) ₹28
6. 6.6 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 11 days (c) 7 days (d) 17 days
7. 7.If 7 notebooks cost ₹91, how much do 3 notebooks cost? (a) ₹273 (b) ₹52 (c) ₹87 (d) ₹39
8. 8.₹84 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹30 (b) ₹42 (c) ₹6 (d) ₹54
9. 9.If 2 pens cost ₹22, how much do 3 pens cost? (a) ₹33 (b) ₹44 (c) ₹66 (d) ₹23
10. 10.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 6 days (d) 7 days
11. 11.₹231 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹147 (b) ₹105 (c) ₹126 (d) ₹21
12. 12.₹315 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹45 (b) ₹270 (c) ₹271 (d) ₹315
13. 13.If 4 mangoes cost ₹40, how much do 3 mangoes cost? (a) ₹39 (b) ₹40 (c) ₹120 (d) ₹30
14. 14.₹195 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹15 (b) ₹135 (c) ₹150 (d) ₹60
15. 15.₹100 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹50 (b) ₹40 (c) ₹20 (d) ₹60
16. 16.3 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 6 days (d) 5 days
17. 17.₹264 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹132 (b) ₹99 (c) ₹33 (d) ₹165
18. 18.If 5 kites cost ₹105, how much do 6 kites cost? (a) ₹106 (b) ₹630 (c) ₹147 (d) ₹126
19. 19.If 9 notebooks cost ₹180, how much do 10 notebooks cost? (a) ₹1800 (b) ₹220 (c) ₹181 (d) ₹200
20. 20.₹135 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹27 (b) ₹108 (c) ₹54 (d) ₹81
21. 21.₹88 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹16 (b) ₹44 (c) ₹72 (d) ₹8
22. 22.6 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 19 days (b) 18 days (c) 14 days (d) 16 days
23. 23.If 4 notebooks cost ₹100, how much do 2 notebooks cost? (a) ₹98 (b) ₹200 (c) ₹50 (d) ₹75
24. 24.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 2 days (b) 18 days (c) 12 days (d) 3 days
25. 25.8 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 13 days (c) 7 days (d) 6 days
26. 26.If 3 pens cost ₹72, how much do 5 pens cost? (a) ₹360 (b) ₹144 (c) ₹74 (d) ₹120
27. 27.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 7 days (d) 4 days
28. 28.₹196 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹28 (b) ₹84 (c) ₹112 (d) ₹98
29. 29.If 2 pens cost ₹32, how much do 9 pens cost? (a) ₹39 (b) ₹288 (c) ₹144 (d) ₹160
30. 30.₹494 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹190 (b) ₹38 (c) ₹304 (d) ₹247
31. 31.If 6 pens cost ₹36, how much do 4 pens cost? (a) ₹24 (b) ₹34 (c) ₹144 (d) ₹30
32. 32.If 8 notebooks cost ₹128, how much do 7 notebooks cost? (a) ₹128 (b) ₹127 (c) ₹112 (d) ₹896
33. 33.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 27 days (b) 9 days (c) 17 days (d) 26 days
34. 34.₹161 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹23 (b) ₹69 (c) ₹115 (d) ₹92
35. 35.If 6 notebooks cost ₹144, how much do 7 notebooks cost? (a) ₹145 (b) ₹192 (c) ₹1008 (d) ₹168
36. 36.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 45 days (c) 5 days (d) 44 days
37. 37.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 45 days (b) 21 days (c) 9 days (d) 5 days
38. 38.₹288 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹144 (b) ₹36 (c) ₹252 (d) ₹288
39. 39.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 15 days (d) 3 days
40. 40.₹330 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹165 (b) ₹30 (c) ₹210 (d) ₹120

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