Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 710 · 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 5 mangoes cost ₹35, how much do 4 mangoes cost? (a) ₹140 (b) ₹35 (c) ₹34 (d) ₹28
2. 2.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 39 days (b) 40 days (c) 9 days (d) 17 days
3. 3.9 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 28 days (c) 27 days (d) 7 days
4. 4.If 9 pens cost ₹45, how much do 8 pens cost? (a) ₹45 (b) ₹44 (c) ₹40 (d) ₹360
5. 5.₹585 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹225 (b) ₹360 (c) ₹45 (d) ₹405
6. 6.If 2 notebooks cost ₹16, how much do 8 notebooks cost? (a) ₹22 (b) ₹128 (c) ₹64 (d) ₹72
7. 7.If 2 mangoes cost ₹38, how much do 6 mangoes cost? (a) ₹228 (b) ₹114 (c) ₹42 (d) ₹133
8. 8.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 21 days (c) 22 days (d) 13 days
9. 9.₹342 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹171 (b) ₹152 (c) ₹190 (d) ₹38
10. 10.₹78 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹39 (b) ₹24 (c) ₹6 (d) ₹54
11. 11.If 2 pens cost ₹28, how much do 11 pens cost? (a) ₹37 (b) ₹154 (c) ₹308 (d) ₹168
12. 12.If 2 pens cost ₹46, how much do 11 pens cost? (a) ₹55 (b) ₹276 (c) ₹253 (d) ₹506
13. 13.If 2 notebooks cost ₹42, how much do 10 notebooks cost? (a) ₹210 (b) ₹50 (c) ₹420 (d) ₹231
14. 14.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 2 days (c) 4 days (d) 9 days
15. 15.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 5 days (c) 6 days (d) 7 days
16. 16.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 6 days (c) 5 days (d) 4 days
17. 17.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 8 days (d) 1 day
18. 18.If 4 notebooks cost ₹32, how much do 8 notebooks cost? (a) ₹36 (b) ₹72 (c) ₹64 (d) ₹256
19. 19.If 6 pens cost ₹132, how much do 10 pens cost? (a) ₹242 (b) ₹136 (c) ₹1320 (d) ₹220
20. 20.9 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 7 days (c) 16 days (d) 15 days
21. 21.₹216 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹24 (b) ₹108 (c) ₹96 (d) ₹120
22. 22.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 12 days (d) 8 days
23. 23.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 21 days (c) 11 days (d) 20 days
24. 24.If 6 mangoes cost ₹126, how much do 3 mangoes cost? (a) ₹378 (b) ₹63 (c) ₹84 (d) ₹123
25. 25.If 2 pens cost ₹48, how much do 3 pens cost? (a) ₹72 (b) ₹144 (c) ₹49 (d) ₹96
26. 26.₹200 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹150 (b) ₹200 (c) ₹50 (d) ₹100
27. 27.If 5 notebooks cost ₹70, how much do 10 notebooks cost? (a) ₹75 (b) ₹700 (c) ₹154 (d) ₹140
28. 28.If 5 mangoes cost ₹120, how much do 7 mangoes cost? (a) ₹168 (b) ₹840 (c) ₹192 (d) ₹122
29. 29.4 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) 7 days (d) 10 days
30. 30.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 11 days (d) 10 days
31. 31.₹200 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹160 (b) ₹100 (c) ₹40 (d) ₹200
32. 32.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 11 days
33. 33.If 3 pens cost ₹57, how much do 4 pens cost? (a) ₹76 (b) ₹228 (c) ₹95 (d) ₹58
34. 34.6 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 31 days (b) 30 days (c) 6 days (d) 14 days
35. 35.If 5 notebooks cost ₹95, how much do 2 notebooks cost? (a) ₹190 (b) ₹38 (c) ₹92 (d) ₹57
36. 36.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 2 days (c) 14 days (d) 10 days
37. 37.If 5 kites cost ₹30, how much do 3 kites cost? (a) ₹24 (b) ₹18 (c) ₹90 (d) ₹28
38. 38.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 4 days (d) 27 days
39. 39.₹507 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹312 (b) ₹351 (c) ₹195 (d) ₹39
40. 40.If 5 kites cost ₹15, how much do 9 kites cost? (a) ₹135 (b) ₹27 (c) ₹30 (d) ₹19

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