Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 899 · 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.₹259 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹185 (b) ₹222 (c) ₹74 (d) ₹37
2. 2.If 8 mangoes cost ₹120, how much do 7 mangoes cost? (a) ₹105 (b) ₹119 (c) ₹120 (d) ₹840
3. 3.If 9 kites cost ₹180, how much do 10 kites cost? (a) ₹181 (b) ₹200 (c) ₹220 (d) ₹1800
4. 4.If 4 mangoes cost ₹92, how much do 3 mangoes cost? (a) ₹92 (b) ₹276 (c) ₹91 (d) ₹69
5. 5.If 9 pens cost ₹72, how much do 3 pens cost? (a) ₹66 (b) ₹216 (c) ₹24 (d) ₹32
6. 6.₹77 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹14 (b) ₹7 (c) ₹70 (d) ₹63
7. 7.If 4 pens cost ₹20, how much do 9 pens cost? (a) ₹180 (b) ₹45 (c) ₹50 (d) ₹25
8. 8.₹473 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹430 (b) ₹86 (c) ₹387 (d) ₹43
9. 9.If 6 kites cost ₹60, how much do 12 kites cost? (a) ₹130 (b) ₹720 (c) ₹66 (d) ₹120
10. 10.9 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 15 days (b) 7 days (c) 13 days (d) 16 days
11. 11.₹319 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹174 (b) ₹29 (c) ₹145 (d) ₹203
12. 12.If 7 mangoes cost ₹49, how much do 9 mangoes cost? (a) ₹70 (b) ₹441 (c) ₹51 (d) ₹63
13. 13.5 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 7 days (d) 11 days
14. 14.If 3 kites cost ₹45, how much do 2 kites cost? (a) ₹30 (b) ₹45 (c) ₹90 (d) ₹44
15. 15.If 5 kites cost ₹15, how much do 9 kites cost? (a) ₹135 (b) ₹30 (c) ₹19 (d) ₹27
16. 16.₹192 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹16 (b) ₹112 (c) ₹80 (d) ₹96
17. 17.If 6 pens cost ₹60, how much do 12 pens cost? (a) ₹120 (b) ₹720 (c) ₹130 (d) ₹66
18. 18.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 3 days (d) 4 days
19. 19.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 49 days (b) 9 days (c) 4 days (d) 19 days
20. 20.If 9 kites cost ₹198, how much do 5 kites cost? (a) ₹132 (b) ₹110 (c) ₹990 (d) ₹194
21. 21.₹96 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹64 (b) ₹32 (c) ₹96 (d) ₹48
22. 22.₹60 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹12 (b) ₹24 (c) ₹30 (d) ₹36
23. 23.₹246 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹205 (b) ₹123 (c) ₹246 (d) ₹41
24. 24.If 6 notebooks cost ₹108, how much do 3 notebooks cost? (a) ₹72 (b) ₹105 (c) ₹54 (d) ₹324
25. 25.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 8 days (d) 2 days
26. 26.If 7 notebooks cost ₹175, how much do 8 notebooks cost? (a) ₹225 (b) ₹1400 (c) ₹200 (d) ₹176
27. 27.If 5 notebooks cost ₹25, how much do 7 notebooks cost? (a) ₹27 (b) ₹40 (c) ₹175 (d) ₹35
28. 28.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 10 days (d) 7 days
29. 29.If 3 pens cost ₹27, how much do 9 pens cost? (a) ₹33 (b) ₹90 (c) ₹81 (d) ₹243
30. 30.₹224 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹16 (b) ₹112 (c) ₹144 (d) ₹80
31. 31.If 5 pens cost ₹35, how much do 9 pens cost? (a) ₹315 (b) ₹39 (c) ₹70 (d) ₹63
32. 32.₹196 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹98 (b) ₹28 (c) ₹84 (d) ₹112
33. 33.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 4 days (d) 3 days
34. 34.If 2 notebooks cost ₹18, how much do 6 notebooks cost? (a) ₹108 (b) ₹22 (c) ₹54 (d) ₹63
35. 35.3 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
36. 36.₹121 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹66 (b) ₹55 (c) ₹77 (d) ₹11
37. 37.₹247 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹171 (b) ₹152 (c) ₹95 (d) ₹19
38. 38.If 5 notebooks cost ₹30, how much do 3 notebooks cost? (a) ₹28 (b) ₹90 (c) ₹18 (d) ₹24
39. 39.₹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
40. 40.4 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) 5 days (d) 18 days

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