Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 68 · 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. 1.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 1 day (d) 11 days
2. 2.₹55 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹45 (b) ₹40 (c) ₹5 (d) ₹15
3. 3.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 12 days (d) 16 days
4. 4.If 2 pens cost ₹34, how much do 9 pens cost? (a) ₹153 (b) ₹306 (c) ₹41 (d) ₹170
5. 5.If 5 mangoes cost ₹30, how much do 3 mangoes cost? (a) ₹24 (b) ₹28 (c) ₹18 (d) ₹90
6. 6.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 2 days (d) 1 day
7. 7.If 2 mangoes cost ₹12, how much do 3 mangoes cost? (a) ₹36 (b) ₹24 (c) ₹13 (d) ₹18
8. 8.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 4 days (d) 6 days
9. 9.If 7 pens cost ₹126, how much do 3 pens cost? (a) ₹378 (b) ₹54 (c) ₹122 (d) ₹72
10. 10.If 3 notebooks cost ₹21, how much do 11 notebooks cost? (a) ₹29 (b) ₹231 (c) ₹77 (d) ₹84
11. 11.If 3 kites cost ₹54, how much do 4 kites cost? (a) ₹72 (b) ₹216 (c) ₹55 (d) ₹90
12. 12.₹650 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹325 (b) ₹250 (c) ₹400 (d) ₹50
13. 13.If 4 pens cost ₹100, how much do 7 pens cost? (a) ₹200 (b) ₹103 (c) ₹700 (d) ₹175
14. 14.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 13 days (d) 25 days
15. 15.If 3 pens cost ₹33, how much do 10 pens cost? (a) ₹121 (b) ₹330 (c) ₹110 (d) ₹40
16. 16.₹154 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹28 (b) ₹77 (c) ₹126 (d) ₹14
17. 17.₹69 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹47 (b) ₹69 (c) ₹23 (d) ₹46
18. 18.₹312 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹26 (b) ₹156 (c) ₹182 (d) ₹130
19. 19.₹396 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹36 (b) ₹324 (c) ₹198 (d) ₹72
20. 20.₹246 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹205 (b) ₹123 (c) ₹246 (d) ₹41
21. 21.8 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 24 days (b) 25 days (c) 4 days (d) 14 days
22. 22.If 4 mangoes cost ₹76, how much do 5 mangoes cost? (a) ₹114 (b) ₹95 (c) ₹77 (d) ₹380
23. 23.If 2 mangoes cost ₹50, how much do 10 mangoes cost? (a) ₹275 (b) ₹500 (c) ₹58 (d) ₹250
24. 24.₹392 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹28 (b) ₹196 (c) ₹252 (d) ₹140
25. 25.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 25 days (d) 9 days
26. 26.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 22 days (d) 21 days
27. 27.₹280 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹20 (b) ₹140 (c) ₹100 (d) ₹180
28. 28.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 19 days (d) 3 days
29. 29.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 11 days (c) 2 days (d) 3 days
30. 30.If 4 mangoes cost ₹16, how much do 3 mangoes cost? (a) ₹15 (b) ₹48 (c) ₹12 (d) ₹16
31. 31.If 7 pens cost ₹147, how much do 8 pens cost? (a) ₹148 (b) ₹1176 (c) ₹189 (d) ₹168
32. 32.₹540 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹270 (b) ₹45 (c) ₹315 (d) ₹225
33. 33.If 8 kites cost ₹192, how much do 7 kites cost? (a) ₹1344 (b) ₹168 (c) ₹191 (d) ₹192
34. 34.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 24 days (b) 16 days (c) 8 days (d) 6 days
35. 35.If 2 pens cost ₹34, how much do 7 pens cost? (a) ₹119 (b) ₹39 (c) ₹238 (d) ₹136
36. 36.₹403 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹31 (b) ₹124 (c) ₹279 (d) ₹310
37. 37.If 5 pens cost ₹35, how much do 8 pens cost? (a) ₹38 (b) ₹63 (c) ₹56 (d) ₹280
38. 38.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 57 days (c) 56 days (d) 8 days
39. 39.If 6 mangoes cost ₹102, how much do 2 mangoes cost? (a) ₹51 (b) ₹34 (c) ₹204 (d) ₹98
40. 40.If 4 kites cost ₹40, how much do 9 kites cost? (a) ₹100 (b) ₹45 (c) ₹360 (d) ₹90

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