Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 258 · 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.₹156 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹91 (b) ₹13 (c) ₹78 (d) ₹65
2. 2.If 8 kites cost ₹24, how much do 3 kites cost? (a) ₹9 (b) ₹19 (c) ₹12 (d) ₹72
3. 3.If 2 mangoes cost ₹32, how much do 4 mangoes cost? (a) ₹34 (b) ₹80 (c) ₹128 (d) ₹64
4. 4.If 9 mangoes cost ₹90, how much do 11 mangoes cost? (a) ₹92 (b) ₹120 (c) ₹990 (d) ₹110
5. 5.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 22 days (c) 21 days (d) 13 days
6. 6.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 15 days (c) 6 days (d) 7 days
7. 7.₹266 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹171 (b) ₹133 (c) ₹19 (d) ₹95
8. 8.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 27 days (d) 26 days
9. 9.If 7 notebooks cost ₹119, how much do 6 notebooks cost? (a) ₹714 (b) ₹119 (c) ₹102 (d) ₹118
10. 10.₹330 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹30 (b) ₹120 (c) ₹210 (d) ₹165
11. 11.If 7 mangoes cost ₹77, how much do 5 mangoes cost? (a) ₹385 (b) ₹75 (c) ₹66 (d) ₹55
12. 12.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 6 days (c) 18 days (d) 48 days
13. 13.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 13 days (d) 6 days
14. 14.If 2 notebooks cost ₹14, how much do 10 notebooks cost? (a) ₹22 (b) ₹70 (c) ₹77 (d) ₹140
15. 15.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 17 days (d) 9 days
16. 16.If 7 mangoes cost ₹126, how much do 10 mangoes cost? (a) ₹1260 (b) ₹180 (c) ₹129 (d) ₹198
17. 17.₹168 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹21 (b) ₹63 (c) ₹84 (d) ₹105
18. 18.If 7 mangoes cost ₹91, how much do 9 mangoes cost? (a) ₹819 (b) ₹93 (c) ₹117 (d) ₹130
19. 19.If 7 notebooks cost ₹49, how much do 6 notebooks cost? (a) ₹294 (b) ₹42 (c) ₹49 (d) ₹48
20. 20.If 8 pens cost ₹64, how much do 6 pens cost? (a) ₹56 (b) ₹48 (c) ₹384 (d) ₹62
21. 21.₹336 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹168 (b) ₹42 (c) ₹210 (d) ₹126
22. 22.₹171 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹114 (b) ₹95 (c) ₹76 (d) ₹19
23. 23.₹341 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹248 (b) ₹31 (c) ₹217 (d) ₹124
24. 24.6 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 22 days (d) 21 days
25. 25.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 5 days (d) 4 days
26. 26.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 7 days (d) 2 days
27. 27.₹296 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹148 (b) ₹37 (c) ₹259 (d) ₹296
28. 28.₹110 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹110 (b) ₹55 (c) ₹11 (d) ₹99
29. 29.₹369 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹329 (b) ₹41 (c) ₹328 (d) ₹369
30. 30.If 3 pens cost ₹18, how much do 6 pens cost? (a) ₹42 (b) ₹36 (c) ₹108 (d) ₹21
31. 31.If 7 kites cost ₹154, how much do 4 kites cost? (a) ₹88 (b) ₹616 (c) ₹151 (d) ₹110
32. 32.If 9 mangoes cost ₹198, how much do 10 mangoes cost? (a) ₹220 (b) ₹199 (c) ₹242 (d) ₹1980
33. 33.9 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 6 days (d) 11 days
34. 34.₹473 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹387 (b) ₹344 (c) ₹43 (d) ₹129
35. 35.₹630 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹315 (b) ₹405 (c) ₹45 (d) ₹225
36. 36.₹130 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹26 (b) ₹130 (c) ₹104 (d) ₹65
37. 37.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 32 days (b) 33 days (c) 17 days (d) 7 days
38. 38.₹65 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹52 (b) ₹65 (c) ₹53 (d) ₹13
39. 39.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 64 days (c) 63 days (d) 7 days
40. 40.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 4 days (d) 1 day

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