Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 623 · 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. 1.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 9 days (d) 7 days
2. 2.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 2 days (c) 11 days (d) 3 days
3. 3.₹429 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹39 (b) ₹273 (c) ₹195 (d) ₹234
4. 4.₹224 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹32 (b) ₹112 (c) ₹96 (d) ₹128
5. 5.If 4 kites cost ₹100, how much do 10 kites cost? (a) ₹106 (b) ₹250 (c) ₹275 (d) ₹1000
6. 6.If 8 mangoes cost ₹80, how much do 12 mangoes cost? (a) ₹960 (b) ₹120 (c) ₹130 (d) ₹84
7. 7.₹180 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹36 (b) ₹90 (c) ₹108 (d) ₹72
8. 8.If 4 mangoes cost ₹100, how much do 5 mangoes cost? (a) ₹125 (b) ₹101 (c) ₹500 (d) ₹150
9. 9.If 5 pens cost ₹85, how much do 10 pens cost? (a) ₹170 (b) ₹187 (c) ₹850 (d) ₹90
10. 10.₹280 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹140 (b) ₹40 (c) ₹160 (d) ₹120
11. 11.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 21 days (c) 9 days (d) 6 days
12. 12.₹98 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹7 (b) ₹63 (c) ₹35 (d) ₹49
13. 13.₹266 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹76 (b) ₹190 (c) ₹133 (d) ₹38
14. 14.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 15 days (c) 9 days (d) 13 days
15. 15.If 2 notebooks cost ₹46, how much do 9 notebooks cost? (a) ₹414 (b) ₹207 (c) ₹230 (d) ₹53
16. 16.If 2 mangoes cost ₹14, how much do 9 mangoes cost? (a) ₹126 (b) ₹63 (c) ₹21 (d) ₹70
17. 17.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 14 days (c) 3 days (d) 4 days
18. 18.₹168 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹21 (b) ₹105 (c) ₹63 (d) ₹84
19. 19.If 5 kites cost ₹25, how much do 9 kites cost? (a) ₹50 (b) ₹225 (c) ₹45 (d) ₹29
20. 20.If 5 kites cost ₹20, how much do 12 kites cost? (a) ₹240 (b) ₹27 (c) ₹48 (d) ₹52
21. 21.If 5 notebooks cost ₹60, how much do 3 notebooks cost? (a) ₹58 (b) ₹180 (c) ₹36 (d) ₹48
22. 22.If 2 notebooks cost ₹38, how much do 5 notebooks cost? (a) ₹95 (b) ₹41 (c) ₹190 (d) ₹114
23. 23.₹123 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹83 (b) ₹82 (c) ₹123 (d) ₹41
24. 24.₹297 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹270 (b) ₹54 (c) ₹243 (d) ₹27
25. 25.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 24 days (d) 6 days
26. 26.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 45 days (c) 5 days (d) 21 days
27. 27.₹252 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹126 (b) ₹180 (c) ₹72 (d) ₹36
28. 28.₹70 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹7 (b) ₹63 (c) ₹70 (d) ₹35
29. 29.If 7 pens cost ₹91, how much do 12 pens cost? (a) ₹169 (b) ₹96 (c) ₹1092 (d) ₹156
30. 30.If 3 pens cost ₹24, how much do 7 pens cost? (a) ₹28 (b) ₹168 (c) ₹64 (d) ₹56
31. 31.If 9 mangoes cost ₹162, how much do 8 mangoes cost? (a) ₹161 (b) ₹144 (c) ₹162 (d) ₹1296
32. 32.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 17 days (c) 2 days (d) 3 days
33. 33.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 13 days (d) 25 days
34. 34.If 9 notebooks cost ₹126, how much do 3 notebooks cost? (a) ₹378 (b) ₹56 (c) ₹120 (d) ₹42
35. 35.6 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 20 days (b) 5 days (c) 13 days (d) 7 days
36. 36.If 3 kites cost ₹15, how much do 8 kites cost? (a) ₹20 (b) ₹40 (c) ₹45 (d) ₹120
37. 37.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 4 days (c) 7 days (d) 3 days
38. 38.If 3 kites cost ₹60, how much do 4 kites cost? (a) ₹61 (b) ₹240 (c) ₹80 (d) ₹100
39. 39.If 4 notebooks cost ₹28, how much do 5 notebooks cost? (a) ₹35 (b) ₹140 (c) ₹29 (d) ₹42
40. 40.₹650 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹50 (b) ₹250 (c) ₹400 (d) ₹325

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