Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 776 · 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.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹84 (b) ₹108 (c) ₹60 (d) ₹12
2. 2.If 6 pens cost ₹42, how much do 9 pens cost? (a) ₹63 (b) ₹45 (c) ₹70 (d) ₹378
3. 3.₹210 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹60 (b) ₹150 (c) ₹105 (d) ₹30
4. 4.If 7 mangoes cost ₹42, how much do 8 mangoes cost? (a) ₹336 (b) ₹48 (c) ₹43 (d) ₹54
5. 5.If 2 notebooks cost ₹6, how much do 4 notebooks cost? (a) ₹12 (b) ₹15 (c) ₹8 (d) ₹24
6. 6.If 8 kites cost ₹152, how much do 12 kites cost? (a) ₹228 (b) ₹1824 (c) ₹247 (d) ₹156
7. 7.₹198 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹144 (b) ₹18 (c) ₹99 (d) ₹54
8. 8.If 6 mangoes cost ₹18, how much do 5 mangoes cost? (a) ₹15 (b) ₹17 (c) ₹18 (d) ₹90
9. 9.₹473 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹387 (b) ₹430 (c) ₹43 (d) ₹86
10. 10.₹550 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹50 (b) ₹275 (c) ₹450 (d) ₹100
11. 11.If 8 kites cost ₹64, how much do 9 kites cost? (a) ₹65 (b) ₹72 (c) ₹80 (d) ₹576
12. 12.₹264 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹33 (b) ₹165 (c) ₹132 (d) ₹99
13. 13.If 4 mangoes cost ₹72, how much do 6 mangoes cost? (a) ₹432 (b) ₹108 (c) ₹74 (d) ₹126
14. 14.If 3 mangoes cost ₹48, how much do 9 mangoes cost? (a) ₹144 (b) ₹160 (c) ₹432 (d) ₹54
15. 15.If 8 kites cost ₹128, how much do 7 kites cost? (a) ₹128 (b) ₹112 (c) ₹896 (d) ₹127
16. 16.If 9 pens cost ₹54, how much do 10 pens cost? (a) ₹60 (b) ₹55 (c) ₹540 (d) ₹66
17. 17.If 9 notebooks cost ₹99, how much do 10 notebooks cost? (a) ₹110 (b) ₹990 (c) ₹121 (d) ₹100
18. 18.If 6 notebooks cost ₹126, how much do 4 notebooks cost? (a) ₹105 (b) ₹504 (c) ₹84 (d) ₹124
19. 19.If 2 pens cost ₹44, how much do 3 pens cost? (a) ₹45 (b) ₹132 (c) ₹66 (d) ₹88
20. 20.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 8 days (d) 2 days
21. 21.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 15 days (c) 13 days (d) 9 days
22. 22.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 18 days (b) 6 days (c) 10 days (d) 7 days
23. 23.₹70 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹28 (b) ₹42 (c) ₹35 (d) ₹14
24. 24.₹264 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹72 (b) ₹24 (c) ₹192 (d) ₹132
25. 25.If 9 pens cost ₹198, how much do 2 pens cost? (a) ₹191 (b) ₹396 (c) ₹44 (d) ₹66
26. 26.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 3 days (c) 15 days (d) 4 days
27. 27.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 5 days (d) 3 days
28. 28.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 6 days (d) 5 days
29. 29.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 18 days (b) 5 days (c) 3 days (d) 4 days
30. 30.₹308 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹220 (b) ₹88 (c) ₹154 (d) ₹44
31. 31.₹99 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹9 (b) ₹72 (c) ₹36 (d) ₹63
32. 32.₹480 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹48 (b) ₹144 (c) ₹240 (d) ₹336
33. 33.If 5 notebooks cost ₹35, how much do 2 notebooks cost? (a) ₹21 (b) ₹32 (c) ₹14 (d) ₹70
34. 34.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 19 days (c) 7 days (d) 40 days
35. 35.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹7 (b) ₹63 (c) ₹56 (d) ₹35
36. 36.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 4 days (d) 2 days
37. 37.If 3 pens cost ₹27, how much do 4 pens cost? (a) ₹108 (b) ₹45 (c) ₹28 (d) ₹36
38. 38.If 9 kites cost ₹180, how much do 5 kites cost? (a) ₹120 (b) ₹176 (c) ₹100 (d) ₹900
39. 39.₹176 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹16 (b) ₹144 (c) ₹88 (d) ₹32
40. 40.If 2 pens cost ₹16, how much do 12 pens cost? (a) ₹104 (b) ₹192 (c) ₹26 (d) ₹96

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