Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 176 · 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 9 kites cost ₹126, how much do 10 kites cost? (a) ₹127 (b) ₹1260 (c) ₹140 (d) ₹154
2. 2.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 13 days (c) 3 days (d) 2 days
3. 3.If 4 mangoes cost ₹88, how much do 3 mangoes cost? (a) ₹87 (b) ₹66 (c) ₹88 (d) ₹264
4. 4.₹414 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹207 (b) ₹184 (c) ₹46 (d) ₹230
5. 5.₹264 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹168 (b) ₹96 (c) ₹24 (d) ₹132
6. 6.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 17 days (d) 28 days
7. 7.₹147 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹42 (b) ₹126 (c) ₹21 (d) ₹105
8. 8.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 7 days (d) 5 days
9. 9.₹238 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹119 (b) ₹34 (c) ₹136 (d) ₹102
10. 10.If 7 kites cost ₹105, how much do 9 kites cost? (a) ₹135 (b) ₹107 (c) ₹945 (d) ₹150
11. 11.If 8 notebooks cost ₹104, how much do 9 notebooks cost? (a) ₹105 (b) ₹936 (c) ₹117 (d) ₹130
12. 12.5 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
13. 13.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 24 days (d) 15 days
14. 14.If 3 pens cost ₹57, how much do 5 pens cost? (a) ₹95 (b) ₹59 (c) ₹285 (d) ₹114
15. 15.5 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 31 days (b) 15 days (c) 30 days (d) 9 days
16. 16.₹280 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹180 (b) ₹140 (c) ₹20 (d) ₹100
17. 17.If 2 kites cost ₹34, how much do 12 kites cost? (a) ₹221 (b) ₹44 (c) ₹204 (d) ₹408
18. 18.If 8 kites cost ₹128, how much do 10 kites cost? (a) ₹130 (b) ₹1280 (c) ₹176 (d) ₹160
19. 19.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 18 days (c) 3 days (d) 14 days
20. 20.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 36 days (b) 35 days (c) 11 days (d) 19 days
21. 21.₹80 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹40 (b) ₹20 (c) ₹80 (d) ₹60
22. 22.₹84 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹42 (b) ₹7 (c) ₹35 (d) ₹49
23. 23.4 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 18 days (b) 8 days (c) 10 days (d) 14 days
24. 24.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 19 days
25. 25.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 16 days (c) 4 days (d) 12 days
26. 26.9 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 8 days (d) 9 days
27. 27.If 6 mangoes cost ₹54, how much do 4 mangoes cost? (a) ₹36 (b) ₹45 (c) ₹52 (d) ₹216
28. 28.If 2 notebooks cost ₹50, how much do 7 notebooks cost? (a) ₹200 (b) ₹55 (c) ₹350 (d) ₹175
29. 29.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 36 days (c) 3 days (d) 37 days
30. 30.If 8 kites cost ₹96, how much do 2 kites cost? (a) ₹192 (b) ₹36 (c) ₹90 (d) ₹24
31. 31.If 3 kites cost ₹15, how much do 6 kites cost? (a) ₹35 (b) ₹30 (c) ₹90 (d) ₹18
32. 32.If 9 pens cost ₹117, how much do 2 pens cost? (a) ₹39 (b) ₹234 (c) ₹110 (d) ₹26
33. 33.₹145 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹29 (b) ₹87 (c) ₹58 (d) ₹116
34. 34.₹88 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹44 (b) ₹8 (c) ₹56 (d) ₹32
35. 35.If 6 notebooks cost ₹120, how much do 9 notebooks cost? (a) ₹1080 (b) ₹123 (c) ₹180 (d) ₹200
36. 36.₹540 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹45 (b) ₹225 (c) ₹270 (d) ₹315
37. 37.₹63 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹7 (b) ₹28 (c) ₹42 (d) ₹35
38. 38.₹450 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹250 (b) ₹225 (c) ₹50 (d) ₹200
39. 39.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 28 days (c) 29 days (d) 3 days
40. 40.If 4 mangoes cost ₹24, how much do 12 mangoes cost? (a) ₹288 (b) ₹78 (c) ₹72 (d) ₹32

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