Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 915 · 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.₹130 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹65 (b) ₹78 (c) ₹26 (d) ₹52
2. 2.If 6 mangoes cost ₹108, how much do 2 mangoes cost? (a) ₹54 (b) ₹104 (c) ₹36 (d) ₹216
3. 3.₹240 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹120 (b) ₹48 (c) ₹240 (d) ₹192
4. 4.If 6 pens cost ₹36, how much do 11 pens cost? (a) ₹41 (b) ₹396 (c) ₹66 (d) ₹72
5. 5.If 7 notebooks cost ₹133, how much do 6 notebooks cost? (a) ₹798 (b) ₹114 (c) ₹133 (d) ₹132
6. 6.If 9 pens cost ₹45, how much do 12 pens cost? (a) ₹540 (b) ₹48 (c) ₹65 (d) ₹60
7. 7.If 5 notebooks cost ₹55, how much do 6 notebooks cost? (a) ₹77 (b) ₹56 (c) ₹66 (d) ₹330
8. 8.₹261 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹261 (b) ₹233 (c) ₹29 (d) ₹232
9. 9.₹245 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹196 (b) ₹147 (c) ₹98 (d) ₹49
10. 10.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 26 days (c) 27 days (d) 13 days
11. 11.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 9 days (d) 3 days
12. 12.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 10 days (b) 1 day (c) 9 days (d) 8 days
13. 13.₹462 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹231 (b) ₹210 (c) ₹42 (d) ₹252
14. 14.If 4 kites cost ₹96, how much do 7 kites cost? (a) ₹192 (b) ₹99 (c) ₹168 (d) ₹672
15. 15.₹297 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹54 (b) ₹270 (c) ₹27 (d) ₹243
16. 16.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 28 days (c) 27 days (d) 3 days
17. 17.₹378 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹294 (b) ₹84 (c) ₹42 (d) ₹189
18. 18.If 2 pens cost ₹46, how much do 6 pens cost? (a) ₹276 (b) ₹161 (c) ₹50 (d) ₹138
19. 19.If 4 kites cost ₹100, how much do 6 kites cost? (a) ₹150 (b) ₹600 (c) ₹175 (d) ₹102
20. 20.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 15 days (d) 18 days
21. 21.If 7 notebooks cost ₹35, how much do 2 notebooks cost? (a) ₹70 (b) ₹10 (c) ₹15 (d) ₹30
22. 22.If 8 kites cost ₹144, how much do 9 kites cost? (a) ₹180 (b) ₹1296 (c) ₹145 (d) ₹162
23. 23.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 5 days (c) 14 days (d) 9 days
24. 24.₹182 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹56 (b) ₹91 (c) ₹14 (d) ₹126
25. 25.₹330 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹60 (b) ₹165 (c) ₹270 (d) ₹30
26. 26.If 2 mangoes cost ₹34, how much do 5 mangoes cost? (a) ₹102 (b) ₹85 (c) ₹170 (d) ₹37
27. 27.₹430 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹43 (b) ₹387 (c) ₹215 (d) ₹430
28. 28.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 34 days (c) 33 days (d) 15 days
29. 29.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 7 days
30. 30.₹585 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹405 (b) ₹45 (c) ₹225 (d) ₹360
31. 31.If 3 pens cost ₹39, how much do 10 pens cost? (a) ₹143 (b) ₹390 (c) ₹46 (d) ₹130
32. 32.6 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 13 days (c) 15 days (d) 12 days
33. 33.₹180 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹40 (b) ₹20 (c) ₹90 (d) ₹140
34. 34.If 2 pens cost ₹22, how much do 3 pens cost? (a) ₹23 (b) ₹66 (c) ₹33 (d) ₹44
35. 35.If 2 notebooks cost ₹44, how much do 5 notebooks cost? (a) ₹110 (b) ₹132 (c) ₹47 (d) ₹220
36. 36.₹328 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹41 (b) ₹164 (c) ₹205 (d) ₹123
37. 37.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 5 days (d) 6 days
38. 38.If 8 pens cost ₹184, how much do 12 pens cost? (a) ₹188 (b) ₹299 (c) ₹276 (d) ₹2208
39. 39.₹128 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹128 (b) ₹64 (c) ₹112 (d) ₹16
40. 40.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 27 days (b) 11 days (c) 19 days (d) 28 days

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