Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 948 · 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 notebooks cost ₹36, how much do 7 notebooks cost? (a) ₹63 (b) ₹39 (c) ₹72 (d) ₹252
2. 2.If 5 pens cost ₹80, how much do 12 pens cost? (a) ₹960 (b) ₹87 (c) ₹192 (d) ₹208
3. 3.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 11 days (d) 4 days
4. 4.6 workers can build a wall in 14 days. How many days will 12 workers take, working at the same speed? (a) 28 days (b) 8 days (c) 7 days (d) 20 days
5. 5.If 4 kites cost ₹36, how much do 10 kites cost? (a) ₹42 (b) ₹99 (c) ₹360 (d) ₹90
6. 6.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 8 days (d) 10 days
7. 7.₹140 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹70 (b) ₹42 (c) ₹14 (d) ₹98
8. 8.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 15 days (c) 21 days (d) 13 days
9. 9.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 2 days (d) 7 days
10. 10.If 9 pens cost ₹117, how much do 11 pens cost? (a) ₹1287 (b) ₹156 (c) ₹143 (d) ₹119
11. 11.If 2 pens cost ₹26, how much do 11 pens cost? (a) ₹35 (b) ₹156 (c) ₹286 (d) ₹143
12. 12.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 15 days (c) 24 days (d) 9 days
13. 13.₹192 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹16 (b) ₹96 (c) ₹112 (d) ₹80
14. 14.If 9 mangoes cost ₹117, how much do 12 mangoes cost? (a) ₹120 (b) ₹169 (c) ₹1404 (d) ₹156
15. 15.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 1 day (b) 3 days (c) 8 days (d) 2 days
16. 16.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 52 days (c) 19 days (d) 53 days
17. 17.₹407 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹37 (b) ₹74 (c) ₹370 (d) ₹333
18. 18.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 3 days (c) 37 days (d) 15 days
19. 19.If 7 mangoes cost ₹154, how much do 5 mangoes cost? (a) ₹152 (b) ₹132 (c) ₹770 (d) ₹110
20. 20.If 3 mangoes cost ₹27, how much do 11 mangoes cost? (a) ₹297 (b) ₹108 (c) ₹99 (d) ₹35
21. 21.If 2 notebooks cost ₹18, how much do 3 notebooks cost? (a) ₹19 (b) ₹27 (c) ₹36 (d) ₹54
22. 22.If 7 notebooks cost ₹168, how much do 3 notebooks cost? (a) ₹96 (b) ₹72 (c) ₹504 (d) ₹164
23. 23.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 5 days (c) 13 days (d) 21 days
24. 24.3 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 5 days (d) 9 days
25. 25.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 4 days (c) 3 days (d) 15 days
26. 26.₹350 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹25 (b) ₹175 (c) ₹125 (d) ₹225
27. 27.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 7 days (d) 2 days
28. 28.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 26 days (d) 27 days
29. 29.₹286 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹110 (b) ₹22 (c) ₹176 (d) ₹143
30. 30.₹132 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹66 (b) ₹12 (c) ₹72 (d) ₹60
31. 31.If 4 kites cost ₹28, how much do 3 kites cost? (a) ₹84 (b) ₹27 (c) ₹28 (d) ₹21
32. 32.If 4 notebooks cost ₹28, how much do 5 notebooks cost? (a) ₹35 (b) ₹29 (c) ₹140 (d) ₹42
33. 33.₹418 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹38 (b) ₹209 (c) ₹228 (d) ₹190
34. 34.If 5 notebooks cost ₹40, how much do 3 notebooks cost? (a) ₹120 (b) ₹38 (c) ₹32 (d) ₹24
35. 35.If 2 kites cost ₹12, how much do 9 kites cost? (a) ₹19 (b) ₹60 (c) ₹108 (d) ₹54
36. 36.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 11 days (c) 22 days (d) 21 days
37. 37.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 15 days (d) 14 days
38. 38.If 5 mangoes cost ₹25, how much do 9 mangoes cost? (a) ₹29 (b) ₹50 (c) ₹45 (d) ₹225
39. 39.8 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 19 days (d) 9 days
40. 40.If 8 pens cost ₹56, how much do 9 pens cost? (a) ₹504 (b) ₹57 (c) ₹63 (d) ₹70

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