Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 260 · 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 14 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 22 days (d) 21 days
2. 2.₹270 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹150 (b) ₹30 (c) ₹120 (d) ₹135
3. 3.8 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 61 days (b) 60 days (c) 9 days (d) 21 days
4. 4.7 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 22 days (b) 15 days (c) 21 days (d) 9 days
5. 5.If 7 mangoes cost ₹84, how much do 2 mangoes cost? (a) ₹79 (b) ₹36 (c) ₹24 (d) ₹168
6. 6.If 8 mangoes cost ₹40, how much do 9 mangoes cost? (a) ₹360 (b) ₹45 (c) ₹41 (d) ₹50
7. 7.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 3 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) 9 days (b) 13 days (c) 3 days (d) 12 days
9. 9.₹70 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹25 (b) ₹45 (c) ₹5 (d) ₹35
10. 10.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 11 days (c) 17 days (d) 19 days
11. 11.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 7 days (b) 12 days (c) 6 days (d) 5 days
12. 12.If 8 pens cost ₹64, how much do 9 pens cost? (a) ₹576 (b) ₹72 (c) ₹80 (d) ₹65
13. 13.₹306 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹170 (b) ₹153 (c) ₹34 (d) ₹136
14. 14.₹286 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹234 (b) ₹52 (c) ₹143 (d) ₹26
15. 15.If 4 notebooks cost ₹48, how much do 2 notebooks cost? (a) ₹96 (b) ₹46 (c) ₹36 (d) ₹24
16. 16.3 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
17. 17.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 8 days (d) 7 days
18. 18.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 45 days (b) 9 days (c) 21 days (d) 5 days
19. 19.If 9 notebooks cost ₹180, how much do 6 notebooks cost? (a) ₹120 (b) ₹140 (c) ₹1080 (d) ₹177
20. 20.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 24 days (b) 4 days (c) 25 days (d) 12 days
21. 21.If 3 kites cost ₹66, how much do 12 kites cost? (a) ₹75 (b) ₹264 (c) ₹792 (d) ₹286
22. 22.₹77 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹11 (b) ₹44 (c) ₹33 (d) ₹55
23. 23.5 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 14 days (c) 10 days (d) 20 days
24. 24.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 1 day
25. 25.8 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 16 days (d) 14 days
26. 26.₹348 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹145 (b) ₹29 (c) ₹203 (d) ₹174
27. 27.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 16 days (c) 12 days (d) 4 days
28. 28.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 30 days (d) 31 days
29. 29.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 14 days (d) 5 days
30. 30.₹248 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹248 (b) ₹31 (c) ₹217 (d) ₹124
31. 31.₹203 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹174 (b) ₹203 (c) ₹29 (d) ₹175
32. 32.If 4 kites cost ₹68, how much do 8 kites cost? (a) ₹153 (b) ₹72 (c) ₹544 (d) ₹136
33. 33.If 4 mangoes cost ₹100, how much do 2 mangoes cost? (a) ₹200 (b) ₹75 (c) ₹50 (d) ₹98
34. 34.If 8 mangoes cost ₹104, how much do 11 mangoes cost? (a) ₹107 (b) ₹1144 (c) ₹156 (d) ₹143
35. 35.If 4 notebooks cost ₹52, how much do 2 notebooks cost? (a) ₹50 (b) ₹104 (c) ₹39 (d) ₹26
36. 36.₹48 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹24 (b) ₹42 (c) ₹6 (d) ₹48
37. 37.If 8 notebooks cost ₹128, how much do 7 notebooks cost? (a) ₹127 (b) ₹128 (c) ₹896 (d) ₹112
38. 38.₹473 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹344 (b) ₹43 (c) ₹172 (d) ₹301
39. 39.₹306 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹34 (b) ₹68 (c) ₹153 (d) ₹238
40. 40.8 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 25 days (b) 4 days (c) 14 days (d) 24 days

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