Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 336 · 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 kites cost ₹18, how much do 11 kites cost? (a) ₹27 (b) ₹108 (c) ₹198 (d) ₹99
2. 2.₹165 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹133 (b) ₹132 (c) ₹33 (d) ₹165
3. 3.₹324 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹27 (b) ₹135 (c) ₹189 (d) ₹162
4. 4.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 18 days (c) 6 days (d) 36 days
5. 5.₹84 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹35 (b) ₹7 (c) ₹42 (d) ₹49
6. 6.If 6 pens cost ₹84, how much do 9 pens cost? (a) ₹140 (b) ₹87 (c) ₹126 (d) ₹756
7. 7.If 4 pens cost ₹60, how much do 5 pens cost? (a) ₹90 (b) ₹75 (c) ₹300 (d) ₹61
8. 8.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 6 days (d) 8 days
9. 9.₹348 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹29 (b) ₹145 (c) ₹174 (d) ₹203
10. 10.If 4 notebooks cost ₹60, how much do 11 notebooks cost? (a) ₹660 (b) ₹67 (c) ₹180 (d) ₹165
11. 11.₹420 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹42 (b) ₹210 (c) ₹420 (d) ₹378
12. 12.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 7 days
13. 13.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 2 days (d) 3 days
14. 14.If 7 mangoes cost ₹28, how much do 4 mangoes cost? (a) ₹25 (b) ₹20 (c) ₹16 (d) ₹112
15. 15.If 2 pens cost ₹26, how much do 3 pens cost? (a) ₹52 (b) ₹78 (c) ₹27 (d) ₹39
16. 16.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 36 days (c) 4 days (d) 18 days
17. 17.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 18 days (c) 12 days (d) 19 days
18. 18.If 4 kites cost ₹48, how much do 10 kites cost? (a) ₹54 (b) ₹120 (c) ₹480 (d) ₹132
19. 19.If 5 pens cost ₹35, how much do 4 pens cost? (a) ₹28 (b) ₹34 (c) ₹35 (d) ₹140
20. 20.₹184 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹184 (b) ₹138 (c) ₹46 (d) ₹92
21. 21.If 2 pens cost ₹14, how much do 11 pens cost? (a) ₹84 (b) ₹23 (c) ₹77 (d) ₹154
22. 22.If 9 notebooks cost ₹216, how much do 5 notebooks cost? (a) ₹120 (b) ₹212 (c) ₹1080 (d) ₹144
23. 23.₹189 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹168 (b) ₹169 (c) ₹21 (d) ₹189
24. 24.9 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
25. 25.₹221 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹68 (b) ₹17 (c) ₹170 (d) ₹153
26. 26.₹476 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹170 (b) ₹34 (c) ₹238 (d) ₹306
27. 27.If 9 pens cost ₹108, how much do 11 pens cost? (a) ₹1188 (b) ₹110 (c) ₹144 (d) ₹132
28. 28.If 5 pens cost ₹110, how much do 6 pens cost? (a) ₹111 (b) ₹660 (c) ₹132 (d) ₹154
29. 29.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 9 days (d) 5 days
30. 30.If 5 pens cost ₹30, how much do 10 pens cost? (a) ₹60 (b) ₹35 (c) ₹300 (d) ₹66
31. 31.₹245 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹35 (b) ₹70 (c) ₹210 (d) ₹175
32. 32.₹322 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹161 (b) ₹92 (c) ₹46 (d) ₹230
33. 33.If 5 mangoes cost ₹60, how much do 7 mangoes cost? (a) ₹84 (b) ₹96 (c) ₹62 (d) ₹420
34. 34.If 5 pens cost ₹85, how much do 4 pens cost? (a) ₹85 (b) ₹84 (c) ₹68 (d) ₹340
35. 35.If 9 mangoes cost ₹36, how much do 12 mangoes cost? (a) ₹432 (b) ₹39 (c) ₹52 (d) ₹48
36. 36.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 7 days (d) 11 days
37. 37.8 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
38. 38.₹170 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹85 (b) ₹68 (c) ₹102 (d) ₹34
39. 39.If 3 kites cost ₹27, how much do 12 kites cost? (a) ₹324 (b) ₹117 (c) ₹36 (d) ₹108
40. 40.6 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 9 days (d) 4 days

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