Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 61 · 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 7 kites cost ₹119, how much do 11 kites cost? (a) ₹204 (b) ₹123 (c) ₹187 (d) ₹1309
2. 2.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 25 days (d) 9 days
3. 3.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 7 days (c) 6 days (d) 8 days
4. 4.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 11 days (d) 14 days
5. 5.If 7 pens cost ₹126, how much do 5 pens cost? (a) ₹124 (b) ₹108 (c) ₹90 (d) ₹630
6. 6.If 7 pens cost ₹105, how much do 11 pens cost? (a) ₹165 (b) ₹180 (c) ₹109 (d) ₹1155
7. 7.₹336 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹192 (b) ₹144 (c) ₹48 (d) ₹168
8. 8.If 3 mangoes cost ₹51, how much do 7 mangoes cost? (a) ₹136 (b) ₹119 (c) ₹55 (d) ₹357
9. 9.₹180 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹90 (b) ₹18 (c) ₹54 (d) ₹126
10. 10.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 21 days (c) 13 days (d) 22 days
11. 11.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 2 days (c) 11 days (d) 8 days
12. 12.If 7 pens cost ₹91, how much do 6 pens cost? (a) ₹546 (b) ₹91 (c) ₹78 (d) ₹90
13. 13.₹559 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹43 (b) ₹430 (c) ₹387 (d) ₹172
14. 14.If 6 notebooks cost ₹30, how much do 5 notebooks cost? (a) ₹29 (b) ₹25 (c) ₹150 (d) ₹30
15. 15.If 9 notebooks cost ₹63, how much do 7 notebooks cost? (a) ₹61 (b) ₹49 (c) ₹56 (d) ₹441
16. 16.₹247 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹171 (b) ₹76 (c) ₹190 (d) ₹19
17. 17.₹99 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹77 (b) ₹88 (c) ₹22 (d) ₹11
18. 18.₹130 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹13 (b) ₹91 (c) ₹65 (d) ₹39
19. 19.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 1 day (c) 3 days (d) 11 days
20. 20.If 5 mangoes cost ₹65, how much do 12 mangoes cost? (a) ₹156 (b) ₹780 (c) ₹72 (d) ₹169
21. 21.₹460 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹138 (b) ₹46 (c) ₹322 (d) ₹230
22. 22.₹130 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹40 (b) ₹65 (c) ₹90 (d) ₹10
23. 23.₹207 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹46 (b) ₹23 (c) ₹184 (d) ₹161
24. 24.If 6 notebooks cost ₹48, how much do 11 notebooks cost? (a) ₹53 (b) ₹528 (c) ₹88 (d) ₹96
25. 25.If 6 mangoes cost ₹120, how much do 7 mangoes cost? (a) ₹160 (b) ₹140 (c) ₹840 (d) ₹121
26. 26.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 37 days (c) 36 days (d) 15 days
27. 27.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 19 days (d) 4 days
28. 28.₹468 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹234 (b) ₹324 (c) ₹144 (d) ₹36
29. 29.If 7 notebooks cost ₹84, how much do 8 notebooks cost? (a) ₹672 (b) ₹85 (c) ₹96 (d) ₹108
30. 30.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 5 days (c) 4 days (d) 6 days
31. 31.₹80 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹56 (b) ₹8 (c) ₹24 (d) ₹40
32. 32.If 9 kites cost ₹189, how much do 6 kites cost? (a) ₹126 (b) ₹186 (c) ₹147 (d) ₹1134
33. 33.₹430 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹215 (b) ₹129 (c) ₹43 (d) ₹301
34. 34.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 11 days (d) 2 days
35. 35.If 6 notebooks cost ₹54, how much do 8 notebooks cost? (a) ₹81 (b) ₹72 (c) ₹56 (d) ₹432
36. 36.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 17 days (c) 34 days (d) 33 days
37. 37.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 16 days (c) 17 days (d) 4 days
38. 38.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 3 days (c) 9 days (d) 4 days
39. 39.If 7 mangoes cost ₹63, how much do 4 mangoes cost? (a) ₹252 (b) ₹45 (c) ₹60 (d) ₹36
40. 40.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 18 days (c) 19 days (d) 12 days

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