Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 822 · 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 6 pens cost ₹60, how much do 7 pens cost? (a) ₹420 (b) ₹80 (c) ₹70 (d) ₹61
2. 2.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 21 days (c) 13 days (d) 22 days
3. 3.₹175 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹175 (b) ₹140 (c) ₹35 (d) ₹141
4. 4.If 5 mangoes cost ₹65, how much do 6 mangoes cost? (a) ₹390 (b) ₹66 (c) ₹91 (d) ₹78
5. 5.If 6 kites cost ₹126, how much do 3 kites cost? (a) ₹123 (b) ₹84 (c) ₹378 (d) ₹63
6. 6.If 5 notebooks cost ₹65, how much do 9 notebooks cost? (a) ₹117 (b) ₹585 (c) ₹130 (d) ₹69
7. 7.₹132 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹77 (b) ₹66 (c) ₹55 (d) ₹11
8. 8.₹175 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹70 (b) ₹105 (c) ₹140 (d) ₹35
9. 9.₹256 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹160 (b) ₹32 (c) ₹96 (d) ₹128
10. 10.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 15 days (d) 14 days
11. 11.If 9 pens cost ₹45, how much do 12 pens cost? (a) ₹60 (b) ₹65 (c) ₹540 (d) ₹48
12. 12.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 16 days (c) 1 day (d) 11 days
13. 13.₹110 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹50 (b) ₹10 (c) ₹60 (d) ₹55
14. 14.₹396 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹44 (b) ₹220 (c) ₹176 (d) ₹198
15. 15.If 3 pens cost ₹24, how much do 5 pens cost? (a) ₹48 (b) ₹40 (c) ₹26 (d) ₹120
16. 16.If 8 mangoes cost ₹104, how much do 3 mangoes cost? (a) ₹99 (b) ₹52 (c) ₹39 (d) ₹312
17. 17.If 7 pens cost ₹126, how much do 2 pens cost? (a) ₹252 (b) ₹54 (c) ₹121 (d) ₹36
18. 18.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 33 days (b) 32 days (c) 14 days (d) 2 days
19. 19.₹188 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹188 (b) ₹47 (c) ₹141 (d) ₹94
20. 20.If 2 notebooks cost ₹46, how much do 9 notebooks cost? (a) ₹414 (b) ₹230 (c) ₹207 (d) ₹53
21. 21.If 4 pens cost ₹88, how much do 2 pens cost? (a) ₹86 (b) ₹176 (c) ₹44 (d) ₹66
22. 22.6 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 31 days (b) 14 days (c) 6 days (d) 30 days
23. 23.If 7 pens cost ₹154, how much do 2 pens cost? (a) ₹308 (b) ₹66 (c) ₹149 (d) ₹44
24. 24.₹192 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹72 (b) ₹96 (c) ₹120 (d) ₹24
25. 25.If 5 mangoes cost ₹120, how much do 4 mangoes cost? (a) ₹96 (b) ₹480 (c) ₹120 (d) ₹119
26. 26.₹70 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹42 (b) ₹28 (c) ₹14 (d) ₹35
27. 27.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 9 days (d) 7 days
28. 28.₹171 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹19 (b) ₹38 (c) ₹152 (d) ₹133
29. 29.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 9 days (d) 7 days
30. 30.₹261 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹174 (b) ₹116 (c) ₹29 (d) ₹145
31. 31.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 25 days (c) 13 days (d) 17 days
32. 32.4 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 16 days (d) 13 days
33. 33.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 52 days (b) 53 days (c) 19 days (d) 7 days
34. 34.If 2 pens cost ₹26, how much do 7 pens cost? (a) ₹182 (b) ₹104 (c) ₹31 (d) ₹91
35. 35.₹144 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹32 (b) ₹72 (c) ₹112 (d) ₹16
36. 36.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 40 days (c) 4 days (d) 41 days
37. 37.₹273 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹189 (b) ₹21 (c) ₹84 (d) ₹210
38. 38.₹84 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹42 (b) ₹84 (c) ₹70 (d) ₹14
39. 39.₹189 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹27 (b) ₹81 (c) ₹135 (d) ₹108
40. 40.If 3 pens cost ₹75, how much do 11 pens cost? (a) ₹275 (b) ₹825 (c) ₹83 (d) ₹300

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