Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 976 · 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. 1.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 19 days
2. 2.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 53 days (c) 7 days (d) 52 days
3. 3.If 5 pens cost ₹25, how much do 8 pens cost? (a) ₹28 (b) ₹200 (c) ₹45 (d) ₹40
4. 4.9 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 28 days (b) 17 days (c) 7 days (d) 27 days
5. 5.₹65 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹52 (b) ₹53 (c) ₹65 (d) ₹13
6. 6.If 5 pens cost ₹20, how much do 2 pens cost? (a) ₹8 (b) ₹40 (c) ₹17 (d) ₹12
7. 7.9 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 18 days (b) 19 days (c) 14 days (d) 6 days
8. 8.6 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 3 days (c) 9 days (d) 13 days
9. 9.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 6 days (d) 7 days
10. 10.₹200 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹25 (b) ₹100 (c) ₹125 (d) ₹75
11. 11.₹105 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹105 (b) ₹84 (c) ₹21 (d) ₹85
12. 12.If 3 notebooks cost ₹9, how much do 12 notebooks cost? (a) ₹39 (b) ₹108 (c) ₹36 (d) ₹18
13. 13.If 6 pens cost ₹42, how much do 5 pens cost? (a) ₹41 (b) ₹42 (c) ₹210 (d) ₹35
14. 14.If 4 mangoes cost ₹96, how much do 6 mangoes cost? (a) ₹98 (b) ₹576 (c) ₹144 (d) ₹168
15. 15.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 28 days (c) 29 days (d) 13 days
16. 16.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 13 days (b) 16 days (c) 11 days (d) 9 days
17. 17.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 3 days (c) 15 days (d) 4 days
18. 18.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 17 days (b) 2 days (c) 4 days (d) 3 days
19. 19.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 17 days (d) 28 days
20. 20.₹42 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹21 (b) ₹42 (c) ₹28 (d) ₹14
21. 21.If 4 notebooks cost ₹44, how much do 12 notebooks cost? (a) ₹528 (b) ₹132 (c) ₹143 (d) ₹52
22. 22.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 34 days (b) 17 days (c) 5 days (d) 33 days
23. 23.₹204 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹102 (b) ₹119 (c) ₹17 (d) ₹85
24. 24.If 2 pens cost ₹22, how much do 9 pens cost? (a) ₹29 (b) ₹110 (c) ₹99 (d) ₹198
25. 25.If 6 mangoes cost ₹138, how much do 8 mangoes cost? (a) ₹207 (b) ₹140 (c) ₹1104 (d) ₹184
26. 26.₹42 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹18 (b) ₹21 (c) ₹6 (d) ₹24
27. 27.If 5 kites cost ₹35, how much do 10 kites cost? (a) ₹350 (b) ₹70 (c) ₹40 (d) ₹77
28. 28.₹299 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹115 (b) ₹207 (c) ₹23 (d) ₹184
29. 29.If 4 kites cost ₹52, how much do 5 kites cost? (a) ₹78 (b) ₹260 (c) ₹53 (d) ₹65
30. 30.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 11 days (d) 10 days
31. 31.4 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) 4 days (d) 10 days
32. 32.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 40 days (b) 39 days (c) 9 days (d) 17 days
33. 33.₹225 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹150 (b) ₹100 (c) ₹125 (d) ₹25
34. 34.₹66 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹66 (b) ₹33 (c) ₹44 (d) ₹22
35. 35.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 12 days (b) 10 days (c) 3 days (d) 2 days
36. 36.If 3 pens cost ₹15, how much do 12 pens cost? (a) ₹24 (b) ₹60 (c) ₹65 (d) ₹180
37. 37.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 9 days (d) 6 days
38. 38.₹230 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹115 (b) ₹46 (c) ₹138 (d) ₹92
39. 39.If 8 kites cost ₹104, how much do 9 kites cost? (a) ₹936 (b) ₹130 (c) ₹117 (d) ₹105
40. 40.If 4 pens cost ₹20, how much do 10 pens cost? (a) ₹200 (b) ₹50 (c) ₹26 (d) ₹55

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