Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 116 · 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.₹528 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹264 (b) ₹48 (c) ₹144 (d) ₹384
2. 2.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 15 days (c) 7 days (d) 6 days
3. 3.If 3 pens cost ₹18, how much do 11 pens cost? (a) ₹26 (b) ₹66 (c) ₹198 (d) ₹72
4. 4.₹495 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹405 (b) ₹45 (c) ₹360 (d) ₹135
5. 5.₹533 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹369 (b) ₹164 (c) ₹41 (d) ₹410
6. 6.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 6 days (c) 48 days (d) 18 days
7. 7.₹150 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹30 (b) ₹75 (c) ₹120 (d) ₹150
8. 8.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 21 days (d) 22 days
9. 9.8 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
10. 10.₹119 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹17 (b) ₹85 (c) ₹51 (d) ₹68
11. 11.If 6 kites cost ₹66, how much do 5 kites cost? (a) ₹330 (b) ₹66 (c) ₹65 (d) ₹55
12. 12.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 25 days (b) 5 days (c) 16 days (d) 4 days
13. 13.₹130 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹65 (b) ₹91 (c) ₹13 (d) ₹39
14. 14.₹135 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹75 (b) ₹90 (c) ₹60 (d) ₹15
15. 15.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 2 days (d) 3 days
16. 16.₹392 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹196 (b) ₹392 (c) ₹343 (d) ₹49
17. 17.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 22 days (c) 1 day (d) 21 days
18. 18.If 4 mangoes cost ₹16, how much do 12 mangoes cost? (a) ₹48 (b) ₹52 (c) ₹24 (d) ₹192
19. 19.₹414 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹207 (b) ₹230 (c) ₹184 (d) ₹46
20. 20.₹484 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹44 (b) ₹132 (c) ₹352 (d) ₹242
21. 21.If 3 notebooks cost ₹27, how much do 10 notebooks cost? (a) ₹99 (b) ₹270 (c) ₹34 (d) ₹90
22. 22.If 4 kites cost ₹80, how much do 5 kites cost? (a) ₹400 (b) ₹81 (c) ₹100 (d) ₹120
23. 23.If 6 pens cost ₹36, how much do 7 pens cost? (a) ₹42 (b) ₹48 (c) ₹37 (d) ₹252
24. 24.₹209 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹76 (b) ₹19 (c) ₹152 (d) ₹133
25. 25.If 4 kites cost ₹40, how much do 12 kites cost? (a) ₹480 (b) ₹48 (c) ₹130 (d) ₹120
26. 26.₹117 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹104 (b) ₹91 (c) ₹26 (d) ₹13
27. 27.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 23 days (b) 8 days (c) 14 days (d) 22 days
28. 28.If 2 mangoes cost ₹20, how much do 5 mangoes cost? (a) ₹100 (b) ₹23 (c) ₹60 (d) ₹50
29. 29.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 1 day (c) 3 days (d) 4 days
30. 30.If 8 pens cost ₹128, how much do 4 pens cost? (a) ₹512 (b) ₹64 (c) ₹80 (d) ₹124
31. 31.If 5 kites cost ₹120, how much do 11 kites cost? (a) ₹126 (b) ₹288 (c) ₹264 (d) ₹1320
32. 32.If 4 notebooks cost ₹16, how much do 7 notebooks cost? (a) ₹19 (b) ₹32 (c) ₹28 (d) ₹112
33. 33.If 4 pens cost ₹32, how much do 9 pens cost? (a) ₹37 (b) ₹72 (c) ₹288 (d) ₹80
34. 34.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 3 days (d) 10 days
35. 35.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 9 days (d) 6 days
36. 36.₹30 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹5 (b) ₹25 (c) ₹15 (d) ₹30
37. 37.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 11 days (c) 15 days (d) 14 days
38. 38.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 9 days (d) 8 days
39. 39.₹114 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹76 (b) ₹38 (c) ₹114 (d) ₹57
40. 40.If 9 kites cost ₹72, how much do 6 kites cost? (a) ₹56 (b) ₹432 (c) ₹48 (d) ₹69

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