Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 576 · 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.₹81 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹45 (b) ₹54 (c) ₹36 (d) ₹9
2. 2.If 8 notebooks cost ₹40, how much do 3 notebooks cost? (a) ₹20 (b) ₹35 (c) ₹120 (d) ₹15
3. 3.If 8 mangoes cost ₹136, how much do 11 mangoes cost? (a) ₹204 (b) ₹1496 (c) ₹187 (d) ₹139
4. 4.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 11 days (d) 26 days
5. 5.If 2 notebooks cost ₹38, how much do 3 notebooks cost? (a) ₹39 (b) ₹57 (c) ₹114 (d) ₹76
6. 6.₹175 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹125 (b) ₹100 (c) ₹25 (d) ₹75
7. 7.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 6 days (d) 9 days
8. 8.₹30 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹30 (b) ₹20 (c) ₹15 (d) ₹10
9. 9.If 3 notebooks cost ₹45, how much do 8 notebooks cost? (a) ₹50 (b) ₹135 (c) ₹120 (d) ₹360
10. 10.6 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 7 days (d) 2 days
11. 11.If 8 mangoes cost ₹56, how much do 5 mangoes cost? (a) ₹53 (b) ₹42 (c) ₹35 (d) ₹280
12. 12.If 3 notebooks cost ₹69, how much do 10 notebooks cost? (a) ₹76 (b) ₹230 (c) ₹253 (d) ₹690
13. 13.₹204 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹102 (b) ₹85 (c) ₹17 (d) ₹119
14. 14.If 3 mangoes cost ₹72, how much do 11 mangoes cost? (a) ₹792 (b) ₹80 (c) ₹288 (d) ₹264
15. 15.If 9 pens cost ₹117, how much do 3 pens cost? (a) ₹111 (b) ₹39 (c) ₹52 (d) ₹351
16. 16.₹77 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹49 (b) ₹56 (c) ₹28 (d) ₹7
17. 17.If 4 kites cost ₹84, how much do 5 kites cost? (a) ₹85 (b) ₹126 (c) ₹420 (d) ₹105
18. 18.If 7 kites cost ₹126, how much do 6 kites cost? (a) ₹125 (b) ₹126 (c) ₹108 (d) ₹756
19. 19.If 2 kites cost ₹14, how much do 9 kites cost? (a) ₹70 (b) ₹21 (c) ₹63 (d) ₹126
20. 20.₹308 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹28 (b) ₹154 (c) ₹252 (d) ₹56
21. 21.₹280 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹200 (b) ₹140 (c) ₹80 (d) ₹40
22. 22.If 7 kites cost ₹168, how much do 10 kites cost? (a) ₹264 (b) ₹171 (c) ₹240 (d) ₹1680
23. 23.If 5 pens cost ₹65, how much do 9 pens cost? (a) ₹585 (b) ₹130 (c) ₹69 (d) ₹117
24. 24.₹342 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹38 (b) ₹76 (c) ₹266 (d) ₹171
25. 25.₹261 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹58 (b) ₹29 (c) ₹203 (d) ₹232
26. 26.₹154 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹126 (b) ₹77 (c) ₹14 (d) ₹28
27. 27.6 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 6 days
28. 28.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 8 days (d) 13 days
29. 29.If 8 mangoes cost ₹192, how much do 7 mangoes cost? (a) ₹191 (b) ₹1344 (c) ₹192 (d) ₹168
30. 30.₹297 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹132 (b) ₹165 (c) ₹198 (d) ₹33
31. 31.If 3 kites cost ₹69, how much do 6 kites cost? (a) ₹414 (b) ₹138 (c) ₹161 (d) ₹72
32. 32.If 3 kites cost ₹42, how much do 9 kites cost? (a) ₹378 (b) ₹140 (c) ₹126 (d) ₹48
33. 33.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 52 days (c) 53 days (d) 19 days
34. 34.6 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 30 days (c) 31 days (d) 12 days
35. 35.₹550 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹275 (b) ₹250 (c) ₹300 (d) ₹50
36. 36.If 4 kites cost ₹68, how much do 12 kites cost? (a) ₹221 (b) ₹816 (c) ₹204 (d) ₹76
37. 37.₹156 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹60 (b) ₹78 (c) ₹96 (d) ₹12
38. 38.If 8 pens cost ₹48, how much do 4 pens cost? (a) ₹30 (b) ₹24 (c) ₹44 (d) ₹192
39. 39.If 4 notebooks cost ₹20, how much do 8 notebooks cost? (a) ₹45 (b) ₹24 (c) ₹40 (d) ₹160
40. 40.If 4 kites cost ₹68, how much do 5 kites cost? (a) ₹69 (b) ₹340 (c) ₹85 (d) ₹102

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