Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 432 · 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. 1.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 1 day (d) 2 days
2. 2.If 9 kites cost ₹153, how much do 3 kites cost? (a) ₹51 (b) ₹68 (c) ₹459 (d) ₹147
3. 3.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 40 days (b) 17 days (c) 9 days (d) 39 days
4. 4.If 8 pens cost ₹192, how much do 12 pens cost? (a) ₹2304 (b) ₹196 (c) ₹312 (d) ₹288
5. 5.If 4 kites cost ₹12, how much do 6 kites cost? (a) ₹72 (b) ₹18 (c) ₹21 (d) ₹14
6. 6.5 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) 3 days (d) 6 days
7. 7.If 2 pens cost ₹18, how much do 12 pens cost? (a) ₹28 (b) ₹117 (c) ₹108 (d) ₹216
8. 8.If 7 mangoes cost ₹28, how much do 5 mangoes cost? (a) ₹26 (b) ₹24 (c) ₹140 (d) ₹20
9. 9.If 2 kites cost ₹12, how much do 12 kites cost? (a) ₹78 (b) ₹144 (c) ₹72 (d) ₹22
10. 10.₹270 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹135 (b) ₹30 (c) ₹120 (d) ₹150
11. 11.₹231 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹84 (b) ₹147 (c) ₹168 (d) ₹21
12. 12.₹121 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹77 (b) ₹11 (c) ₹66 (d) ₹55
13. 13.₹30 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹10 (b) ₹20 (c) ₹15 (d) ₹30
14. 14.6 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 14 days (b) 8 days (c) 18 days (d) 10 days
15. 15.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 7 days (b) 12 days (c) 6 days (d) 5 days
16. 16.₹374 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹187 (b) ₹34 (c) ₹68 (d) ₹306
17. 17.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 7 days (d) 1 day
18. 18.₹270 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹135 (b) ₹240 (c) ₹270 (d) ₹30
19. 19.₹56 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹42 (b) ₹28 (c) ₹14 (d) ₹56
20. 20.₹120 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹36 (b) ₹84 (c) ₹12 (d) ₹60
21. 21.₹273 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹156 (b) ₹39 (c) ₹117 (d) ₹195
22. 22.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 27 days (c) 28 days (d) 15 days
23. 23.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 32 days (c) 33 days (d) 7 days
24. 24.If 5 pens cost ₹115, how much do 10 pens cost? (a) ₹120 (b) ₹253 (c) ₹1150 (d) ₹230
25. 25.If 5 mangoes cost ₹85, how much do 4 mangoes cost? (a) ₹68 (b) ₹84 (c) ₹340 (d) ₹85
26. 26.If 8 notebooks cost ₹144, how much do 5 notebooks cost? (a) ₹720 (b) ₹141 (c) ₹108 (d) ₹90
27. 27.If 2 notebooks cost ₹38, how much do 6 notebooks cost? (a) ₹228 (b) ₹42 (c) ₹133 (d) ₹114
28. 28.If 5 kites cost ₹60, how much do 4 kites cost? (a) ₹48 (b) ₹60 (c) ₹59 (d) ₹240
29. 29.If 8 pens cost ₹48, how much do 9 pens cost? (a) ₹49 (b) ₹60 (c) ₹432 (d) ₹54
30. 30.If 6 pens cost ₹48, how much do 4 pens cost? (a) ₹46 (b) ₹40 (c) ₹32 (d) ₹192
31. 31.₹117 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹81 (b) ₹9 (c) ₹45 (d) ₹72
32. 32.₹429 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹297 (b) ₹132 (c) ₹33 (d) ₹330
33. 33.If 4 kites cost ₹20, how much do 10 kites cost? (a) ₹26 (b) ₹200 (c) ₹50 (d) ₹55
34. 34.If 9 pens cost ₹198, how much do 4 pens cost? (a) ₹193 (b) ₹88 (c) ₹110 (d) ₹792
35. 35.If 2 notebooks cost ₹12, how much do 12 notebooks cost? (a) ₹144 (b) ₹22 (c) ₹78 (d) ₹72
36. 36.₹234 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹26 (b) ₹117 (c) ₹182 (d) ₹52
37. 37.If 5 pens cost ₹55, how much do 10 pens cost? (a) ₹60 (b) ₹550 (c) ₹110 (d) ₹121
38. 38.₹230 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹184 (b) ₹46 (c) ₹230 (d) ₹115
39. 39.₹630 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹315 (b) ₹225 (c) ₹45 (d) ₹405
40. 40.If 9 notebooks cost ₹72, how much do 5 notebooks cost? (a) ₹48 (b) ₹40 (c) ₹68 (d) ₹360

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