Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 705 · 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 8 pens cost ₹184, how much do 11 pens cost? (a) ₹276 (b) ₹2024 (c) ₹253 (d) ₹187
2. 2.₹611 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹47 (b) ₹188 (c) ₹423 (d) ₹470
3. 3.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 1 day (c) 17 days (d) 10 days
4. 4.If 4 pens cost ₹76, how much do 8 pens cost? (a) ₹171 (b) ₹152 (c) ₹80 (d) ₹608
5. 5.If 6 mangoes cost ₹90, how much do 10 mangoes cost? (a) ₹94 (b) ₹165 (c) ₹900 (d) ₹150
6. 6.If 2 pens cost ₹48, how much do 8 pens cost? (a) ₹216 (b) ₹384 (c) ₹192 (d) ₹54
7. 7.₹228 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹38 (b) ₹114 (c) ₹228 (d) ₹190
8. 8.₹396 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹231 (b) ₹33 (c) ₹165 (d) ₹198
9. 9.If 8 mangoes cost ₹64, how much do 5 mangoes cost? (a) ₹320 (b) ₹40 (c) ₹48 (d) ₹61
10. 10.₹266 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹95 (b) ₹171 (c) ₹19 (d) ₹133
11. 11.If 4 mangoes cost ₹24, how much do 2 mangoes cost? (a) ₹18 (b) ₹12 (c) ₹48 (d) ₹22
12. 12.If 8 pens cost ₹200, how much do 2 pens cost? (a) ₹50 (b) ₹75 (c) ₹194 (d) ₹400
13. 13.If 9 pens cost ₹54, how much do 7 pens cost? (a) ₹378 (b) ₹52 (c) ₹48 (d) ₹42
14. 14.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 21 days (b) 9 days (c) 5 days (d) 45 days
15. 15.₹234 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹117 (b) ₹18 (c) ₹162 (d) ₹72
16. 16.₹220 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹80 (b) ₹140 (c) ₹110 (d) ₹20
17. 17.₹290 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹290 (b) ₹29 (c) ₹145 (d) ₹261
18. 18.6 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 9 days (d) 25 days
19. 19.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 1 day (d) 8 days
20. 20.If 4 kites cost ₹72, how much do 9 kites cost? (a) ₹77 (b) ₹162 (c) ₹648 (d) ₹180
21. 21.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 16 days (c) 7 days (d) 28 days
22. 22.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 3 days (d) 18 days
23. 23.₹495 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹90 (b) ₹405 (c) ₹450 (d) ₹45
24. 24.If 9 pens cost ₹225, how much do 5 pens cost? (a) ₹150 (b) ₹221 (c) ₹125 (d) ₹1125
25. 25.₹350 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹175 (b) ₹225 (c) ₹125 (d) ₹25
26. 26.5 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 31 days (b) 9 days (c) 30 days (d) 15 days
27. 27.₹288 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹144 (b) ₹224 (c) ₹32 (d) ₹64
28. 28.If 6 mangoes cost ₹150, how much do 8 mangoes cost? (a) ₹225 (b) ₹200 (c) ₹1200 (d) ₹152
29. 29.If 2 kites cost ₹24, how much do 8 kites cost? (a) ₹96 (b) ₹30 (c) ₹108 (d) ₹192
30. 30.8 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 20 days (c) 41 days (d) 40 days
31. 31.If 7 mangoes cost ₹77, how much do 8 mangoes cost? (a) ₹88 (b) ₹616 (c) ₹99 (d) ₹78
32. 32.₹546 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹42 (b) ₹336 (c) ₹273 (d) ₹210
33. 33.If 6 notebooks cost ₹132, how much do 3 notebooks cost? (a) ₹129 (b) ₹88 (c) ₹66 (d) ₹396
34. 34.₹300 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹25 (b) ₹150 (c) ₹175 (d) ₹125
35. 35.₹198 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹18 (b) ₹36 (c) ₹99 (d) ₹162
36. 36.If 8 mangoes cost ₹184, how much do 7 mangoes cost? (a) ₹184 (b) ₹183 (c) ₹1288 (d) ₹161
37. 37.₹504 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹210 (b) ₹42 (c) ₹294 (d) ₹252
38. 38.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 24 days (b) 25 days (c) 12 days (d) 23 days
39. 39.₹112 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹16 (b) ₹32 (c) ₹56 (d) ₹80
40. 40.If 9 notebooks cost ₹90, how much do 2 notebooks cost? (a) ₹30 (b) ₹180 (c) ₹83 (d) ₹20

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