Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 27 · 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 kites cost ₹30, how much do 12 kites cost? (a) ₹360 (b) ₹37 (c) ₹78 (d) ₹72
2. 2.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 12 days (c) 3 days (d) 1 day
3. 3.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 3 days (d) 10 days
4. 4.If 3 mangoes cost ₹48, how much do 4 mangoes cost? (a) ₹49 (b) ₹64 (c) ₹192 (d) ₹80
5. 5.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 11 days (c) 2 days (d) 3 days
6. 6.If 8 notebooks cost ₹168, how much do 9 notebooks cost? (a) ₹169 (b) ₹1512 (c) ₹210 (d) ₹189
7. 7.If 3 pens cost ₹9, how much do 4 pens cost? (a) ₹15 (b) ₹10 (c) ₹12 (d) ₹36
8. 8.₹312 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹312 (b) ₹39 (c) ₹273 (d) ₹156
9. 9.₹315 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹35 (b) ₹210 (c) ₹140 (d) ₹175
10. 10.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 28 days (c) 17 days (d) 7 days
11. 11.If 9 mangoes cost ₹180, how much do 11 mangoes cost? (a) ₹182 (b) ₹240 (c) ₹220 (d) ₹1980
12. 12.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 5 days (c) 14 days (d) 9 days
13. 13.If 9 pens cost ₹27, how much do 2 pens cost? (a) ₹20 (b) ₹9 (c) ₹6 (d) ₹54
14. 14.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 3 days (d) 4 days
15. 15.If 5 kites cost ₹60, how much do 6 kites cost? (a) ₹84 (b) ₹61 (c) ₹360 (d) ₹72
16. 16.₹273 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹189 (b) ₹168 (c) ₹21 (d) ₹105
17. 17.3 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 48 days (d) 21 days
18. 18.If 7 pens cost ₹126, how much do 2 pens cost? (a) ₹252 (b) ₹54 (c) ₹121 (d) ₹36
19. 19.If 9 mangoes cost ₹63, how much do 10 mangoes cost? (a) ₹64 (b) ₹77 (c) ₹630 (d) ₹70
20. 20.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 5 days (d) 4 days
21. 21.If 5 pens cost ₹65, how much do 9 pens cost? (a) ₹585 (b) ₹130 (c) ₹69 (d) ₹117
22. 22.₹90 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹45 (b) ₹63 (c) ₹9 (d) ₹27
23. 23.₹63 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹7 (b) ₹35 (c) ₹42 (d) ₹28
24. 24.If 8 notebooks cost ₹64, how much do 2 notebooks cost? (a) ₹58 (b) ₹16 (c) ₹24 (d) ₹128
25. 25.₹299 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹184 (b) ₹23 (c) ₹115 (d) ₹207
26. 26.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 13 days (d) 11 days
27. 27.₹462 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹297 (b) ₹165 (c) ₹231 (d) ₹33
28. 28.If 3 pens cost ₹9, how much do 7 pens cost? (a) ₹21 (b) ₹24 (c) ₹63 (d) ₹13
29. 29.₹90 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹18 (b) ₹54 (c) ₹45 (d) ₹36
30. 30.If 3 mangoes cost ₹42, how much do 12 mangoes cost? (a) ₹182 (b) ₹168 (c) ₹504 (d) ₹51
31. 31.If 3 mangoes cost ₹9, how much do 4 mangoes cost? (a) ₹36 (b) ₹15 (c) ₹12 (d) ₹10
32. 32.₹54 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹12 (b) ₹27 (c) ₹6 (d) ₹42
33. 33.₹48 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹24 (b) ₹18 (c) ₹6 (d) ₹30
34. 34.If 9 pens cost ₹207, how much do 3 pens cost? (a) ₹201 (b) ₹92 (c) ₹621 (d) ₹69
35. 35.₹253 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹207 (b) ₹23 (c) ₹184 (d) ₹69
36. 36.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 2 days (c) 12 days (d) 3 days
37. 37.If 3 pens cost ₹51, how much do 7 pens cost? (a) ₹119 (b) ₹357 (c) ₹136 (d) ₹55
38. 38.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 17 days (d) 6 days
39. 39.If 9 mangoes cost ₹207, how much do 10 mangoes cost? (a) ₹208 (b) ₹253 (c) ₹2070 (d) ₹230
40. 40.8 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) 10 days (d) 17 days

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