Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 32 · 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. 1.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 15 days (d) 8 days
2. 2.₹350 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹50 (b) ₹150 (c) ₹200 (d) ₹175
3. 3.If 3 mangoes cost ₹42, how much do 2 mangoes cost? (a) ₹84 (b) ₹41 (c) ₹28 (d) ₹42
4. 4.If 7 notebooks cost ₹105, how much do 2 notebooks cost? (a) ₹45 (b) ₹30 (c) ₹210 (d) ₹100
5. 5.If 7 notebooks cost ₹112, how much do 2 notebooks cost? (a) ₹224 (b) ₹32 (c) ₹48 (d) ₹107
6. 6.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 27 days (d) 28 days
7. 7.5 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 13 days (d) 10 days
8. 8.₹264 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹110 (b) ₹132 (c) ₹22 (d) ₹154
9. 9.If 6 pens cost ₹78, how much do 9 pens cost? (a) ₹702 (b) ₹117 (c) ₹81 (d) ₹130
10. 10.₹190 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹76 (b) ₹95 (c) ₹38 (d) ₹114
11. 11.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 12 days (c) 3 days (d) 2 days
12. 12.If 2 pens cost ₹24, how much do 4 pens cost? (a) ₹96 (b) ₹48 (c) ₹60 (d) ₹26
13. 13.If 9 notebooks cost ₹162, how much do 8 notebooks cost? (a) ₹1296 (b) ₹161 (c) ₹144 (d) ₹162
14. 14.₹374 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹204 (b) ₹187 (c) ₹170 (d) ₹34
15. 15.₹396 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹72 (b) ₹324 (c) ₹198 (d) ₹36
16. 16.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 10 days (d) 1 day
17. 17.₹182 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹78 (b) ₹104 (c) ₹26 (d) ₹91
18. 18.If 5 mangoes cost ₹105, how much do 6 mangoes cost? (a) ₹126 (b) ₹630 (c) ₹147 (d) ₹106
19. 19.₹286 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹234 (b) ₹52 (c) ₹143 (d) ₹26
20. 20.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 49 days (d) 9 days
21. 21.If 4 pens cost ₹16, how much do 6 pens cost? (a) ₹24 (b) ₹96 (c) ₹28 (d) ₹18
22. 22.If 7 pens cost ₹77, how much do 12 pens cost? (a) ₹132 (b) ₹924 (c) ₹82 (d) ₹143
23. 23.If 2 pens cost ₹12, how much do 3 pens cost? (a) ₹24 (b) ₹18 (c) ₹13 (d) ₹36
24. 24.₹288 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹224 (b) ₹64 (c) ₹144 (d) ₹32
25. 25.₹484 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹176 (b) ₹44 (c) ₹242 (d) ₹308
26. 26.₹120 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹60 (b) ₹36 (c) ₹84 (d) ₹12
27. 27.₹120 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹60 (b) ₹20 (c) ₹100 (d) ₹120
28. 28.₹585 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹225 (b) ₹45 (c) ₹405 (d) ₹360
29. 29.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 11 days (c) 21 days (d) 19 days
30. 30.If 3 kites cost ₹12, how much do 4 kites cost? (a) ₹13 (b) ₹48 (c) ₹16 (d) ₹20
31. 31.₹182 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹14 (b) ₹126 (c) ₹91 (d) ₹56
32. 32.₹495 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹270 (b) ₹225 (c) ₹315 (d) ₹45
33. 33.If 8 notebooks cost ₹64, how much do 5 notebooks cost? (a) ₹48 (b) ₹61 (c) ₹320 (d) ₹40
34. 34.₹128 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹64 (b) ₹128 (c) ₹96 (d) ₹32
35. 35.7 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) 8 days (d) 6 days
36. 36.If 5 notebooks cost ₹25, how much do 8 notebooks cost? (a) ₹40 (b) ₹200 (c) ₹28 (d) ₹45
37. 37.If 2 mangoes cost ₹46, how much do 5 mangoes cost? (a) ₹115 (b) ₹138 (c) ₹49 (d) ₹230
38. 38.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 17 days (d) 16 days
39. 39.7 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) 1 day (d) 7 days
40. 40.₹187 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹119 (b) ₹85 (c) ₹102 (d) ₹17

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