Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 11 · 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.₹574 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹205 (b) ₹287 (c) ₹41 (d) ₹369
2. 2.If 6 pens cost ₹48, how much do 2 pens cost? (a) ₹44 (b) ₹24 (c) ₹96 (d) ₹16
3. 3.If 9 pens cost ₹117, how much do 4 pens cost? (a) ₹112 (b) ₹468 (c) ₹52 (d) ₹65
4. 4.₹490 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹49 (b) ₹441 (c) ₹245 (d) ₹490
5. 5.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 7 days (d) 5 days
6. 6.₹324 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹162 (b) ₹27 (c) ₹135 (d) ₹189
7. 7.₹416 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹128 (b) ₹288 (c) ₹208 (d) ₹32
8. 8.₹66 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹33 (b) ₹44 (c) ₹66 (d) ₹22
9. 9.₹35 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹35 (b) ₹7 (c) ₹28 (d) ₹29
10. 10.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 1 day (c) 16 days (d) 9 days
11. 11.If 8 notebooks cost ₹128, how much do 3 notebooks cost? (a) ₹64 (b) ₹384 (c) ₹123 (d) ₹48
12. 12.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 10 days (c) 17 days (d) 11 days
13. 13.₹560 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹200 (b) ₹40 (c) ₹360 (d) ₹280
14. 14.₹598 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹368 (b) ₹46 (c) ₹230 (d) ₹299
15. 15.₹63 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹42 (b) ₹28 (c) ₹7 (d) ₹35
16. 16.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 45 days (b) 21 days (c) 5 days (d) 9 days
17. 17.₹148 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹74 (b) ₹148 (c) ₹111 (d) ₹37
18. 18.If 5 kites cost ₹70, how much do 4 kites cost? (a) ₹280 (b) ₹69 (c) ₹70 (d) ₹56
19. 19.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 2 days (c) 33 days (d) 32 days
20. 20.If 7 mangoes cost ₹35, how much do 4 mangoes cost? (a) ₹32 (b) ₹140 (c) ₹20 (d) ₹25
21. 21.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 8 days (d) 1 day
22. 22.If 3 pens cost ₹15, how much do 8 pens cost? (a) ₹20 (b) ₹45 (c) ₹120 (d) ₹40
23. 23.₹378 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹189 (b) ₹243 (c) ₹135 (d) ₹27
24. 24.If 4 notebooks cost ₹20, how much do 5 notebooks cost? (a) ₹25 (b) ₹30 (c) ₹21 (d) ₹100
25. 25.₹528 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹264 (b) ₹48 (c) ₹384 (d) ₹144
26. 26.₹650 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹50 (b) ₹325 (c) ₹400 (d) ₹250
27. 27.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 5 days (c) 4 days (d) 12 days
28. 28.If 3 pens cost ₹24, how much do 4 pens cost? (a) ₹96 (b) ₹32 (c) ₹40 (d) ₹25
29. 29.₹168 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹168 (b) ₹84 (c) ₹126 (d) ₹42
30. 30.₹24 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹8 (b) ₹12 (c) ₹24 (d) ₹16
31. 31.₹20 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹10 (b) ₹15 (c) ₹5 (d) ₹20
32. 32.₹462 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹33 (b) ₹165 (c) ₹297 (d) ₹231
33. 33.₹238 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹34 (b) ₹119 (c) ₹136 (d) ₹102
34. 34.If 2 pens cost ₹50, how much do 9 pens cost? (a) ₹250 (b) ₹225 (c) ₹57 (d) ₹450
35. 35.9 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 54 days (c) 55 days (d) 5 days
36. 36.₹160 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹80 (b) ₹16 (c) ₹48 (d) ₹112
37. 37.If 4 kites cost ₹60, how much do 8 kites cost? (a) ₹135 (b) ₹64 (c) ₹120 (d) ₹480
38. 38.If 9 pens cost ₹189, how much do 4 pens cost? (a) ₹184 (b) ₹756 (c) ₹84 (d) ₹105
39. 39.₹396 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹216 (b) ₹180 (c) ₹198 (d) ₹36
40. 40.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 3 days (d) 4 days

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