Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 642 · 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 4 pens cost ₹36, how much do 11 pens cost? (a) ₹43 (b) ₹108 (c) ₹396 (d) ₹99
2. 2.If 8 pens cost ₹96, how much do 9 pens cost? (a) ₹108 (b) ₹120 (c) ₹864 (d) ₹97
3. 3.3 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 32 days (b) 17 days (c) 3 days (d) 2 days
4. 4.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 9 days (d) 17 days
5. 5.₹176 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹80 (b) ₹88 (c) ₹96 (d) ₹16
6. 6.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 12 days (d) 8 days
7. 7.If 6 kites cost ₹150, how much do 10 kites cost? (a) ₹1500 (b) ₹154 (c) ₹250 (d) ₹275
8. 8.If 5 pens cost ₹105, how much do 4 pens cost? (a) ₹104 (b) ₹84 (c) ₹420 (d) ₹105
9. 9.If 8 notebooks cost ₹72, how much do 12 notebooks cost? (a) ₹117 (b) ₹76 (c) ₹108 (d) ₹864
10. 10.₹624 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹432 (b) ₹312 (c) ₹48 (d) ₹192
11. 11.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 28 days (c) 19 days (d) 27 days
12. 12.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 3 days (d) 2 days
13. 13.If 6 mangoes cost ₹24, how much do 11 mangoes cost? (a) ₹29 (b) ₹264 (c) ₹48 (d) ₹44
14. 14.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 10 days (c) 16 days (d) 4 days
15. 15.₹598 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹46 (b) ₹299 (c) ₹184 (d) ₹414
16. 16.₹52 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹13 (b) ₹39 (c) ₹26 (d) ₹52
17. 17.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 3 days (c) 12 days (d) 11 days
18. 18.If 9 mangoes cost ₹162, how much do 6 mangoes cost? (a) ₹126 (b) ₹159 (c) ₹108 (d) ₹972
19. 19.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 17 days (d) 16 days
20. 20.If 5 notebooks cost ₹115, how much do 6 notebooks cost? (a) ₹116 (b) ₹690 (c) ₹138 (d) ₹161
21. 21.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 32 days (b) 33 days (c) 2 days (d) 14 days
22. 22.9 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 18 days (c) 13 days (d) 19 days
23. 23.₹180 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹160 (b) ₹90 (c) ₹20 (d) ₹180
24. 24.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 17 days (d) 6 days
25. 25.If 4 mangoes cost ₹56, how much do 5 mangoes cost? (a) ₹280 (b) ₹84 (c) ₹57 (d) ₹70
26. 26.₹80 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹64 (b) ₹40 (c) ₹80 (d) ₹16
27. 27.If 9 pens cost ₹27, how much do 3 pens cost? (a) ₹12 (b) ₹9 (c) ₹81 (d) ₹21
28. 28.₹297 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹162 (b) ₹189 (c) ₹27 (d) ₹135
29. 29.If 2 kites cost ₹34, how much do 11 kites cost? (a) ₹43 (b) ₹374 (c) ₹204 (d) ₹187
30. 30.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 16 days (d) 7 days
31. 31.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 26 days (c) 27 days (d) 11 days
32. 32.₹517 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹47 (b) ₹423 (c) ₹94 (d) ₹470
33. 33.₹160 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹80 (b) ₹120 (c) ₹40 (d) ₹160
34. 34.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 28 days (d) 18 days
35. 35.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 10 days (d) 4 days
36. 36.₹210 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹120 (b) ₹90 (c) ₹30 (d) ₹105
37. 37.₹506 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹46 (b) ₹253 (c) ₹276 (d) ₹230
38. 38.₹252 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹126 (b) ₹180 (c) ₹72 (d) ₹36
39. 39.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 40 days (c) 7 days (d) 19 days
40. 40.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 49 days (c) 19 days (d) 4 days

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