Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 688 · 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 3 mangoes cost ₹18, how much do 5 mangoes cost? (a) ₹20 (b) ₹90 (c) ₹36 (d) ₹30
2. 2.₹384 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹160 (b) ₹192 (c) ₹224 (d) ₹32
3. 3.If 8 notebooks cost ₹88, how much do 12 notebooks cost? (a) ₹132 (b) ₹1056 (c) ₹143 (d) ₹92
4. 4.9 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 2 days (c) 25 days (d) 24 days
5. 5.₹407 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹148 (b) ₹37 (c) ₹259 (d) ₹296
6. 6.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 25 days (d) 13 days
7. 7.₹432 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹48 (b) ₹192 (c) ₹240 (d) ₹216
8. 8.If 7 notebooks cost ₹133, how much do 5 notebooks cost? (a) ₹131 (b) ₹665 (c) ₹114 (d) ₹95
9. 9.If 7 pens cost ₹175, how much do 10 pens cost? (a) ₹178 (b) ₹275 (c) ₹250 (d) ₹1750
10. 10.₹343 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹147 (b) ₹196 (c) ₹245 (d) ₹49
11. 11.₹220 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹88 (b) ₹110 (c) ₹44 (d) ₹132
12. 12.₹119 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹17 (b) ₹68 (c) ₹85 (d) ₹51
13. 13.If 2 notebooks cost ₹40, how much do 7 notebooks cost? (a) ₹45 (b) ₹280 (c) ₹160 (d) ₹140
14. 14.If 3 pens cost ₹48, how much do 7 pens cost? (a) ₹52 (b) ₹112 (c) ₹336 (d) ₹128
15. 15.If 6 pens cost ₹150, how much do 5 pens cost? (a) ₹150 (b) ₹750 (c) ₹125 (d) ₹149
16. 16.If 2 notebooks cost ₹32, how much do 9 notebooks cost? (a) ₹39 (b) ₹288 (c) ₹160 (d) ₹144
17. 17.₹96 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹12 (b) ₹84 (c) ₹48 (d) ₹96
18. 18.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹56 (b) ₹63 (c) ₹7 (d) ₹35
19. 19.₹207 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹115 (b) ₹23 (c) ₹92 (d) ₹138
20. 20.₹24 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹6 (b) ₹18 (c) ₹24 (d) ₹12
21. 21.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 8 days (d) 12 days
22. 22.If 6 kites cost ₹114, how much do 2 kites cost? (a) ₹228 (b) ₹57 (c) ₹110 (d) ₹38
23. 23.8 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 7 days (c) 12 days (d) 11 days
24. 24.If 6 pens cost ₹144, how much do 4 pens cost? (a) ₹120 (b) ₹96 (c) ₹576 (d) ₹142
25. 25.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 5 days (c) 8 days (d) 9 days
26. 26.9 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 18 days (b) 9 days (c) 15 days (d) 8 days
27. 27.If 4 notebooks cost ₹60, how much do 2 notebooks cost? (a) ₹120 (b) ₹30 (c) ₹58 (d) ₹45
28. 28.₹378 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹189 (b) ₹135 (c) ₹243 (d) ₹27
29. 29.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 3 days (d) 8 days
30. 30.₹360 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹180 (b) ₹40 (c) ₹360 (d) ₹320
31. 31.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 8 days (c) 12 days (d) 11 days
32. 32.₹44 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹22 (b) ₹11 (c) ₹44 (d) ₹33
33. 33.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 21 days (c) 22 days (d) 15 days
34. 34.₹50 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹25 (b) ₹40 (c) ₹10 (d) ₹50
35. 35.₹434 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹217 (b) ₹31 (c) ₹279 (d) ₹155
36. 36.₹341 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹155 (b) ₹217 (c) ₹31 (d) ₹186
37. 37.₹39 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹27 (b) ₹13 (c) ₹26 (d) ₹39
38. 38.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 16 days (c) 15 days (d) 11 days
39. 39.₹56 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹7 (b) ₹35 (c) ₹28 (d) ₹21
40. 40.If 2 mangoes cost ₹26, how much do 3 mangoes cost? (a) ₹52 (b) ₹27 (c) ₹39 (d) ₹78

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