Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 992 · 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 5 kites cost ₹20, how much do 6 kites cost? (a) ₹120 (b) ₹24 (c) ₹28 (d) ₹21
2. 2.If 8 pens cost ₹168, how much do 5 pens cost? (a) ₹840 (b) ₹165 (c) ₹126 (d) ₹105
3. 3.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 12 days (c) 3 days (d) 2 days
4. 4.If 2 pens cost ₹10, how much do 9 pens cost? (a) ₹90 (b) ₹50 (c) ₹45 (d) ₹17
5. 5.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 10 days (c) 11 days (d) 8 days
6. 6.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 1 day (c) 36 days (d) 37 days
7. 7.If 2 notebooks cost ₹24, how much do 9 notebooks cost? (a) ₹31 (b) ₹120 (c) ₹216 (d) ₹108
8. 8.If 4 pens cost ₹72, how much do 10 pens cost? (a) ₹180 (b) ₹198 (c) ₹78 (d) ₹720
9. 9.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 15 days (d) 9 days
10. 10.If 7 kites cost ₹35, how much do 10 kites cost? (a) ₹350 (b) ₹38 (c) ₹55 (d) ₹50
11. 11.If 2 notebooks cost ₹20, how much do 3 notebooks cost? (a) ₹21 (b) ₹60 (c) ₹30 (d) ₹40
12. 12.If 4 mangoes cost ₹76, how much do 2 mangoes cost? (a) ₹74 (b) ₹57 (c) ₹152 (d) ₹38
13. 13.₹351 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹156 (b) ₹234 (c) ₹195 (d) ₹39
14. 14.If 9 kites cost ₹54, how much do 6 kites cost? (a) ₹42 (b) ₹36 (c) ₹324 (d) ₹51
15. 15.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 11 days (d) 4 days
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) 6 days (d) 7 days
17. 17.₹245 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹175 (b) ₹35 (c) ₹210 (d) ₹70
18. 18.If 6 notebooks cost ₹102, how much do 11 notebooks cost? (a) ₹204 (b) ₹1122 (c) ₹187 (d) ₹107
19. 19.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 8 days (c) 12 days (d) 20 days
20. 20.If 8 pens cost ₹176, how much do 5 pens cost? (a) ₹132 (b) ₹880 (c) ₹173 (d) ₹110
21. 21.₹91 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹7 (b) ₹28 (c) ₹70 (d) ₹63
22. 22.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 9 days
23. 23.If 5 mangoes cost ₹100, how much do 9 mangoes cost? (a) ₹200 (b) ₹104 (c) ₹900 (d) ₹180
24. 24.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 13 days (c) 28 days (d) 29 days
25. 25.₹384 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹144 (b) ₹192 (c) ₹48 (d) ₹240
26. 26.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 5 days (d) 3 days
27. 27.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 6 days (d) 17 days
28. 28.₹70 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹21 (b) ₹7 (c) ₹49 (d) ₹35
29. 29.₹420 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹210 (b) ₹270 (c) ₹150 (d) ₹30
30. 30.9 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 14 days (b) 19 days (c) 18 days (d) 6 days
31. 31.If 8 kites cost ₹80, how much do 12 kites cost? (a) ₹960 (b) ₹84 (c) ₹130 (d) ₹120
32. 32.₹279 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹124 (b) ₹186 (c) ₹155 (d) ₹31
33. 33.If 5 pens cost ₹115, how much do 9 pens cost? (a) ₹230 (b) ₹119 (c) ₹1035 (d) ₹207
34. 34.₹27 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹18 (b) ₹9 (c) ₹19 (d) ₹27
35. 35.If 4 pens cost ₹96, how much do 2 pens cost? (a) ₹192 (b) ₹72 (c) ₹94 (d) ₹48
36. 36.₹176 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹22 (b) ₹88 (c) ₹154 (d) ₹176
37. 37.If 6 pens cost ₹24, how much do 11 pens cost? (a) ₹264 (b) ₹48 (c) ₹29 (d) ₹44
38. 38.₹40 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹5 (b) ₹15 (c) ₹25 (d) ₹20
39. 39.₹187 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹153 (b) ₹17 (c) ₹51 (d) ₹136
40. 40.₹125 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹50 (b) ₹100 (c) ₹75 (d) ₹25

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