Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 950 · 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.₹440 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹220 (b) ₹40 (c) ₹360 (d) ₹80
2. 2.If 8 pens cost ₹192, how much do 6 pens cost? (a) ₹144 (b) ₹190 (c) ₹168 (d) ₹1152
3. 3.₹598 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹184 (b) ₹46 (c) ₹414 (d) ₹299
4. 4.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 16 days (d) 11 days
5. 5.If 8 mangoes cost ₹104, how much do 2 mangoes cost? (a) ₹208 (b) ₹98 (c) ₹39 (d) ₹26
6. 6.₹117 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹72 (b) ₹81 (c) ₹9 (d) ₹45
7. 7.₹78 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹48 (b) ₹30 (c) ₹39 (d) ₹6
8. 8.5 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) 9 days (d) 6 days
9. 9.₹245 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹147 (b) ₹98 (c) ₹49 (d) ₹196
10. 10.₹407 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹259 (b) ₹296 (c) ₹148 (d) ₹37
11. 11.₹308 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹132 (b) ₹154 (c) ₹176 (d) ₹44
12. 12.If 9 pens cost ₹90, how much do 6 pens cost? (a) ₹70 (b) ₹540 (c) ₹60 (d) ₹87
13. 13.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 1 day (b) 10 days (c) 9 days (d) 8 days
14. 14.₹301 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹43 (b) ₹129 (c) ₹172 (d) ₹215
15. 15.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 45 days (c) 21 days (d) 5 days
16. 16.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 15 days (c) 4 days (d) 14 days
17. 17.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 18 days (c) 19 days (d) 17 days
18. 18.₹156 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹12 (b) ₹60 (c) ₹78 (d) ₹96
19. 19.If 3 pens cost ₹18, how much do 6 pens cost? (a) ₹42 (b) ₹21 (c) ₹36 (d) ₹108
20. 20.If 6 kites cost ₹132, how much do 5 kites cost? (a) ₹131 (b) ₹660 (c) ₹132 (d) ₹110
21. 21.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 16 days (c) 28 days (d) 12 days
22. 22.₹243 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹217 (b) ₹27 (c) ₹243 (d) ₹216
23. 23.If 6 notebooks cost ₹48, how much do 3 notebooks cost? (a) ₹45 (b) ₹32 (c) ₹24 (d) ₹144
24. 24.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 9 days (c) 8 days (d) 2 days
25. 25.If 3 pens cost ₹42, how much do 2 pens cost? (a) ₹42 (b) ₹41 (c) ₹28 (d) ₹84
26. 26.₹207 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹46 (b) ₹184 (c) ₹161 (d) ₹23
27. 27.₹484 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹132 (b) ₹352 (c) ₹242 (d) ₹44
28. 28.If 3 mangoes cost ₹39, how much do 5 mangoes cost? (a) ₹65 (b) ₹195 (c) ₹78 (d) ₹41
29. 29.₹198 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹54 (b) ₹18 (c) ₹144 (d) ₹99
30. 30.₹198 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹99 (b) ₹90 (c) ₹18 (d) ₹108
31. 31.6 workers can build a wall in 10 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 16 days (d) 20 days
32. 32.If 5 mangoes cost ₹55, how much do 6 mangoes cost? (a) ₹330 (b) ₹56 (c) ₹77 (d) ₹66
33. 33.₹637 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹49 (b) ₹392 (c) ₹245 (d) ₹441
34. 34.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 1 day (d) 11 days
35. 35.₹310 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹310 (b) ₹31 (c) ₹279 (d) ₹155
36. 36.7 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
37. 37.If 3 notebooks cost ₹18, how much do 6 notebooks cost? (a) ₹21 (b) ₹42 (c) ₹36 (d) ₹108
38. 38.₹90 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹80 (b) ₹10 (c) ₹45 (d) ₹90
39. 39.If 7 pens cost ₹84, how much do 4 pens cost? (a) ₹48 (b) ₹60 (c) ₹336 (d) ₹81
40. 40.If 6 pens cost ₹108, how much do 4 pens cost? (a) ₹72 (b) ₹90 (c) ₹106 (d) ₹432

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