Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 24 · 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. 1.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 11 days (c) 17 days (d) 35 days
2. 2.₹33 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹22 (b) ₹33 (c) ₹11 (d) ₹23
3. 3.If 6 kites cost ₹84, how much do 8 kites cost? (a) ₹86 (b) ₹672 (c) ₹126 (d) ₹112
4. 4.If 8 pens cost ₹48, how much do 12 pens cost? (a) ₹576 (b) ₹52 (c) ₹72 (d) ₹78
5. 5.₹616 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹44 (b) ₹308 (c) ₹396 (d) ₹220
6. 6.₹363 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹132 (b) ₹33 (c) ₹231 (d) ₹264
7. 7.9 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 7 days (d) 17 days
8. 8.₹224 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹140 (b) ₹84 (c) ₹28 (d) ₹112
9. 9.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 4 days (c) 3 days (d) 27 days
10. 10.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 13 days
11. 11.₹56 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹7 (b) ₹56 (c) ₹49 (d) ₹28
12. 12.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 4 days (c) 6 days (d) 36 days
13. 13.If 4 pens cost ₹12, how much do 8 pens cost? (a) ₹16 (b) ₹96 (c) ₹24 (d) ₹27
14. 14.If 5 mangoes cost ₹50, how much do 6 mangoes cost? (a) ₹51 (b) ₹300 (c) ₹70 (d) ₹60
15. 15.If 9 pens cost ₹126, how much do 8 pens cost? (a) ₹125 (b) ₹112 (c) ₹1008 (d) ₹126
16. 16.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 7 days (d) 6 days
17. 17.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 3 days (d) 9 days
18. 18.₹250 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹175 (b) ₹25 (c) ₹125 (d) ₹75
19. 19.If 4 kites cost ₹60, how much do 10 kites cost? (a) ₹165 (b) ₹600 (c) ₹150 (d) ₹66
20. 20.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 13 days (d) 1 day
21. 21.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 22 days (c) 11 days (d) 21 days
22. 22.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 14 days (d) 13 days
23. 23.If 9 pens cost ₹225, how much do 6 pens cost? (a) ₹222 (b) ₹150 (c) ₹175 (d) ₹1350
24. 24.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 19 days (b) 28 days (c) 9 days (d) 7 days
25. 25.If 2 notebooks cost ₹10, how much do 3 notebooks cost? (a) ₹30 (b) ₹11 (c) ₹20 (d) ₹15
26. 26.₹121 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹11 (b) ₹44 (c) ₹88 (d) ₹77
27. 27.₹210 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹105 (b) ₹120 (c) ₹90 (d) ₹30
28. 28.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 5 days (d) 10 days
29. 29.If 3 pens cost ₹18, how much do 2 pens cost? (a) ₹18 (b) ₹36 (c) ₹12 (d) ₹17
30. 30.₹189 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹84 (b) ₹105 (c) ₹21 (d) ₹126
31. 31.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 12 days (c) 3 days (d) 1 day
32. 32.If 7 pens cost ₹168, how much do 8 pens cost? (a) ₹169 (b) ₹1344 (c) ₹216 (d) ₹192
33. 33.₹104 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹52 (b) ₹64 (c) ₹40 (d) ₹8
34. 34.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 12 days (b) 16 days (c) 5 days (d) 4 days
35. 35.If 4 pens cost ₹32, how much do 9 pens cost? (a) ₹80 (b) ₹72 (c) ₹37 (d) ₹288
36. 36.₹182 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹56 (b) ₹126 (c) ₹14 (d) ₹91
37. 37.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 22 days (c) 13 days (d) 23 days
38. 38.₹252 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹126 (b) ₹252 (c) ₹42 (d) ₹210
39. 39.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 13 days (c) 6 days (d) 7 days
40. 40.If 9 notebooks cost ₹99, how much do 12 notebooks cost? (a) ₹102 (b) ₹1188 (c) ₹143 (d) ₹132

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