Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 979 · 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 ₹72, how much do 6 pens cost? (a) ₹63 (b) ₹70 (c) ₹432 (d) ₹54
2. 2.₹336 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹210 (b) ₹126 (c) ₹168 (d) ₹42
3. 3.₹100 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹100 (b) ₹50 (c) ₹10 (d) ₹90
4. 4.₹392 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹196 (b) ₹28 (c) ₹252 (d) ₹140
5. 5.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 9 days (c) 11 days (d) 10 days
6. 6.₹315 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹225 (b) ₹135 (c) ₹180 (d) ₹45
7. 7.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 6 days (d) 2 days
8. 8.₹273 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹235 (b) ₹234 (c) ₹39 (d) ₹273
9. 9.If 4 mangoes cost ₹76, how much do 10 mangoes cost? (a) ₹760 (b) ₹209 (c) ₹190 (d) ₹82
10. 10.If 7 mangoes cost ₹42, how much do 6 mangoes cost? (a) ₹36 (b) ₹41 (c) ₹42 (d) ₹252
11. 11.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 1 day
12. 12.If 2 notebooks cost ₹28, how much do 4 notebooks cost? (a) ₹112 (b) ₹30 (c) ₹56 (d) ₹70
13. 13.If 3 notebooks cost ₹48, how much do 4 notebooks cost? (a) ₹64 (b) ₹49 (c) ₹80 (d) ₹192
14. 14.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 43 days (b) 8 days (c) 20 days (d) 42 days
15. 15.₹495 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹270 (b) ₹45 (c) ₹315 (d) ₹225
16. 16.If 5 notebooks cost ₹80, how much do 7 notebooks cost? (a) ₹112 (b) ₹128 (c) ₹82 (d) ₹560
17. 17.₹66 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹6 (b) ₹33 (c) ₹12 (d) ₹54
18. 18.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 28 days (c) 29 days (d) 3 days
19. 19.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 13 days (d) 10 days
20. 20.If 3 notebooks cost ₹21, how much do 5 notebooks cost? (a) ₹42 (b) ₹105 (c) ₹35 (d) ₹23
21. 21.If 6 kites cost ₹132, how much do 2 kites cost? (a) ₹264 (b) ₹128 (c) ₹66 (d) ₹44
22. 22.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 16 days (c) 9 days (d) 15 days
23. 23.₹136 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹17 (b) ₹68 (c) ₹85 (d) ₹51
24. 24.If 8 mangoes cost ₹32, how much do 7 mangoes cost? (a) ₹28 (b) ₹224 (c) ₹31 (d) ₹32
25. 25.If 2 notebooks cost ₹46, how much do 5 notebooks cost? (a) ₹49 (b) ₹138 (c) ₹230 (d) ₹115
26. 26.₹248 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹155 (b) ₹31 (c) ₹93 (d) ₹124
27. 27.If 2 pens cost ₹14, how much do 8 pens cost? (a) ₹20 (b) ₹112 (c) ₹63 (d) ₹56
28. 28.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 2 days (d) 4 days
29. 29.If 9 mangoes cost ₹126, how much do 3 mangoes cost? (a) ₹56 (b) ₹378 (c) ₹120 (d) ₹42
30. 30.If 7 mangoes cost ₹70, how much do 12 mangoes cost? (a) ₹130 (b) ₹840 (c) ₹75 (d) ₹120
31. 31.If 3 mangoes cost ₹24, how much do 2 mangoes cost? (a) ₹48 (b) ₹24 (c) ₹16 (d) ₹23
32. 32.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 6 days (c) 10 days (d) 4 days
33. 33.If 9 notebooks cost ₹225, how much do 5 notebooks cost? (a) ₹221 (b) ₹150 (c) ₹125 (d) ₹1125
34. 34.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 8 days (d) 2 days
35. 35.₹225 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹225 (b) ₹201 (c) ₹25 (d) ₹200
36. 36.₹108 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹12 (b) ₹60 (c) ₹48 (d) ₹54
37. 37.If 7 pens cost ₹70, how much do 9 pens cost? (a) ₹72 (b) ₹90 (c) ₹100 (d) ₹630
38. 38.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 3 days (d) 10 days
39. 39.If 9 pens cost ₹45, how much do 2 pens cost? (a) ₹15 (b) ₹90 (c) ₹10 (d) ₹38
40. 40.₹170 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹102 (b) ₹34 (c) ₹85 (d) ₹68

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