Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 124 · 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. 1.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 9 days (d) 5 days
2. 2.If 6 mangoes cost ₹30, how much do 9 mangoes cost? (a) ₹270 (b) ₹50 (c) ₹33 (d) ₹45
3. 3.If 7 mangoes cost ₹42, how much do 8 mangoes cost? (a) ₹54 (b) ₹48 (c) ₹43 (d) ₹336
4. 4.If 8 pens cost ₹176, how much do 12 pens cost? (a) ₹264 (b) ₹2112 (c) ₹286 (d) ₹180
5. 5.₹24 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹24 (b) ₹12 (c) ₹18 (d) ₹6
6. 6.₹363 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹165 (b) ₹231 (c) ₹198 (d) ₹33
7. 7.If 5 mangoes cost ₹110, how much do 3 mangoes cost? (a) ₹88 (b) ₹108 (c) ₹66 (d) ₹330
8. 8.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 6 days (c) 8 days (d) 7 days
9. 9.If 4 pens cost ₹32, how much do 10 pens cost? (a) ₹88 (b) ₹38 (c) ₹80 (d) ₹320
10. 10.₹184 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹23 (b) ₹92 (c) ₹69 (d) ₹115
11. 11.₹36 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹36 (b) ₹12 (c) ₹18 (d) ₹24
12. 12.If 5 mangoes cost ₹90, how much do 2 mangoes cost? (a) ₹180 (b) ₹36 (c) ₹54 (d) ₹87
13. 13.If 3 pens cost ₹72, how much do 10 pens cost? (a) ₹240 (b) ₹79 (c) ₹264 (d) ₹720
14. 14.If 5 mangoes cost ₹115, how much do 11 mangoes cost? (a) ₹253 (b) ₹1265 (c) ₹276 (d) ₹121
15. 15.3 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 32 days (b) 17 days (c) 2 days (d) 3 days
16. 16.₹546 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹273 (b) ₹336 (c) ₹210 (d) ₹42
17. 17.₹462 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹168 (b) ₹42 (c) ₹231 (d) ₹294
18. 18.₹91 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹78 (b) ₹13 (c) ₹65 (d) ₹26
19. 19.If 3 mangoes cost ₹45, how much do 12 mangoes cost? (a) ₹54 (b) ₹180 (c) ₹195 (d) ₹540
20. 20.If 6 kites cost ₹48, how much do 7 kites cost? (a) ₹64 (b) ₹56 (c) ₹336 (d) ₹49
21. 21.₹441 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹98 (b) ₹49 (c) ₹392 (d) ₹343
22. 22.₹77 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹7 (b) ₹49 (c) ₹35 (d) ₹42
23. 23.If 5 pens cost ₹115, how much do 2 pens cost? (a) ₹230 (b) ₹112 (c) ₹46 (d) ₹69
24. 24.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 16 days (d) 11 days
25. 25.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 7 days (c) 16 days (d) 11 days
26. 26.₹264 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹33 (b) ₹165 (c) ₹99 (d) ₹132
27. 27.₹210 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹168 (b) ₹42 (c) ₹105 (d) ₹210
28. 28.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 24 days (b) 6 days (c) 9 days (d) 15 days
29. 29.If 6 mangoes cost ₹60, how much do 2 mangoes cost? (a) ₹20 (b) ₹120 (c) ₹30 (d) ₹56
30. 30.If 3 pens cost ₹21, how much do 5 pens cost? (a) ₹105 (b) ₹35 (c) ₹23 (d) ₹42
31. 31.₹418 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹38 (b) ₹209 (c) ₹266 (d) ₹152
32. 32.If 3 kites cost ₹42, how much do 2 kites cost? (a) ₹42 (b) ₹28 (c) ₹84 (d) ₹41
33. 33.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 5 days (d) 14 days
34. 34.If 4 pens cost ₹24, how much do 5 pens cost? (a) ₹25 (b) ₹120 (c) ₹36 (d) ₹30
35. 35.₹363 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹99 (b) ₹297 (c) ₹33 (d) ₹264
36. 36.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹35 (b) ₹56 (c) ₹63 (d) ₹7
37. 37.If 3 notebooks cost ₹24, how much do 5 notebooks cost? (a) ₹120 (b) ₹26 (c) ₹48 (d) ₹40
38. 38.If 6 notebooks cost ₹126, how much do 9 notebooks cost? (a) ₹129 (b) ₹210 (c) ₹189 (d) ₹1134
39. 39.If 9 kites cost ₹216, how much do 12 kites cost? (a) ₹2592 (b) ₹219 (c) ₹312 (d) ₹288
40. 40.6 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 20 days (b) 7 days (c) 5 days (d) 13 days

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