Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 10 · 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 8 kites cost ₹160, how much do 7 kites cost? (a) ₹160 (b) ₹140 (c) ₹1120 (d) ₹159
2. 2.₹60 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹12 (b) ₹36 (c) ₹30 (d) ₹24
3. 3.If 5 mangoes cost ₹70, how much do 3 mangoes cost? (a) ₹56 (b) ₹68 (c) ₹42 (d) ₹210
4. 4.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 3 days (d) 4 days
5. 5.₹168 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹98 (b) ₹14 (c) ₹70 (d) ₹84
6. 6.If 2 notebooks cost ₹34, how much do 7 notebooks cost? (a) ₹119 (b) ₹136 (c) ₹238 (d) ₹39
7. 7.₹143 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹65 (b) ₹78 (c) ₹91 (d) ₹13
8. 8.₹504 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹294 (b) ₹252 (c) ₹210 (d) ₹42
9. 9.₹264 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹33 (b) ₹132 (c) ₹99 (d) ₹165
10. 10.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 7 days (d) 12 days
11. 11.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 12 days (d) 20 days
12. 12.If 4 pens cost ₹92, how much do 5 pens cost? (a) ₹138 (b) ₹93 (c) ₹115 (d) ₹460
13. 13.₹351 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹195 (b) ₹39 (c) ₹234 (d) ₹156
14. 14.If 7 pens cost ₹70, how much do 8 pens cost? (a) ₹80 (b) ₹90 (c) ₹71 (d) ₹560
15. 15.If 8 kites cost ₹72, how much do 3 kites cost? (a) ₹36 (b) ₹67 (c) ₹27 (d) ₹216
16. 16.₹220 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹100 (b) ₹110 (c) ₹20 (d) ₹120
17. 17.₹248 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹124 (b) ₹155 (c) ₹31 (d) ₹93
18. 18.If 7 mangoes cost ₹91, how much do 12 mangoes cost? (a) ₹169 (b) ₹1092 (c) ₹156 (d) ₹96
19. 19.₹234 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹26 (b) ₹117 (c) ₹234 (d) ₹208
20. 20.₹376 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹376 (b) ₹47 (c) ₹188 (d) ₹329
21. 21.If 4 notebooks cost ₹16, how much do 2 notebooks cost? (a) ₹32 (b) ₹8 (c) ₹12 (d) ₹14
22. 22.₹266 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹133 (b) ₹190 (c) ₹76 (d) ₹38
23. 23.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 7 days (d) 4 days
24. 24.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 36 days (b) 35 days (c) 19 days (d) 11 days
25. 25.If 8 pens cost ₹200, how much do 12 pens cost? (a) ₹204 (b) ₹2400 (c) ₹325 (d) ₹300
26. 26.5 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 10 days (c) 20 days (d) 21 days
27. 27.₹276 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹115 (b) ₹23 (c) ₹161 (d) ₹138
28. 28.If 9 kites cost ₹54, how much do 7 kites cost? (a) ₹378 (b) ₹48 (c) ₹52 (d) ₹42
29. 29.If 5 kites cost ₹45, how much do 6 kites cost? (a) ₹63 (b) ₹46 (c) ₹54 (d) ₹270
30. 30.₹238 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹34 (b) ₹102 (c) ₹136 (d) ₹119
31. 31.If 5 mangoes cost ₹105, how much do 9 mangoes cost? (a) ₹109 (b) ₹210 (c) ₹945 (d) ₹189
32. 32.₹130 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹65 (b) ₹13 (c) ₹39 (d) ₹91
33. 33.If 9 pens cost ₹36, how much do 10 pens cost? (a) ₹40 (b) ₹44 (c) ₹37 (d) ₹360
34. 34.₹286 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹130 (b) ₹26 (c) ₹156 (d) ₹143
35. 35.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 7 days (c) 19 days (d) 40 days
36. 36.6 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 16 days (c) 5 days (d) 6 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) 9 days (c) 5 days (d) 21 days
38. 38.₹45 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹18 (b) ₹9 (c) ₹36 (d) ₹27
39. 39.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 7 days (d) 3 days
40. 40.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 4 days (d) 17 days

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