Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 525 · 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.If 7 kites cost ₹91, how much do 2 kites cost? (a) ₹182 (b) ₹39 (c) ₹26 (d) ₹86
2. 2.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 5 days (d) 8 days
3. 3.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 7 days (d) 8 days
4. 4.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 18 days (b) 7 days (c) 6 days (d) 10 days
5. 5.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 9 days (d) 8 days
6. 6.If 7 notebooks cost ₹140, how much do 3 notebooks cost? (a) ₹60 (b) ₹136 (c) ₹420 (d) ₹80
7. 7.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 4 days (d) 27 days
8. 8.₹252 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹108 (b) ₹144 (c) ₹126 (d) ₹36
9. 9.If 5 mangoes cost ₹20, how much do 4 mangoes cost? (a) ₹16 (b) ₹80 (c) ₹20 (d) ₹19
10. 10.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 18 days (c) 10 days (d) 28 days
11. 11.₹234 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹117 (b) ₹144 (c) ₹18 (d) ₹90
12. 12.₹432 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹48 (b) ₹192 (c) ₹216 (d) ₹240
13. 13.If 6 notebooks cost ₹114, how much do 10 notebooks cost? (a) ₹118 (b) ₹209 (c) ₹1140 (d) ₹190
14. 14.If 5 notebooks cost ₹60, how much do 11 notebooks cost? (a) ₹132 (b) ₹66 (c) ₹660 (d) ₹144
15. 15.₹528 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹264 (b) ₹288 (c) ₹48 (d) ₹240
16. 16.If 4 notebooks cost ₹68, how much do 9 notebooks cost? (a) ₹612 (b) ₹170 (c) ₹153 (d) ₹73
17. 17.If 4 notebooks cost ₹24, how much do 7 notebooks cost? (a) ₹168 (b) ₹48 (c) ₹27 (d) ₹42
18. 18.₹77 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹66 (b) ₹11 (c) ₹55 (d) ₹22
19. 19.₹91 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹13 (b) ₹79 (c) ₹91 (d) ₹78
20. 20.If 9 notebooks cost ₹153, how much do 7 notebooks cost? (a) ₹136 (b) ₹1071 (c) ₹119 (d) ₹151
21. 21.₹216 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹108 (b) ₹48 (c) ₹168 (d) ₹24
22. 22.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 40 days (b) 9 days (c) 39 days (d) 17 days
23. 23.If 2 notebooks cost ₹36, how much do 6 notebooks cost? (a) ₹216 (b) ₹40 (c) ₹126 (d) ₹108
24. 24.₹104 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹8 (b) ₹52 (c) ₹32 (d) ₹72
25. 25.₹286 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹143 (b) ₹130 (c) ₹26 (d) ₹156
26. 26.If 5 pens cost ₹40, how much do 10 pens cost? (a) ₹80 (b) ₹45 (c) ₹88 (d) ₹400
27. 27.If 4 pens cost ₹36, how much do 6 pens cost? (a) ₹38 (b) ₹63 (c) ₹216 (d) ₹54
28. 28.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 2 days (d) 4 days
29. 29.₹88 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹64 (b) ₹24 (c) ₹44 (d) ₹8
30. 30.₹72 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹8 (b) ₹56 (c) ₹16 (d) ₹36
31. 31.₹429 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹297 (b) ₹165 (c) ₹33 (d) ₹264
32. 32.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 2 days (c) 18 days (d) 3 days
33. 33.₹78 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹39 (b) ₹48 (c) ₹6 (d) ₹30
34. 34.If 3 notebooks cost ₹63, how much do 4 notebooks cost? (a) ₹105 (b) ₹64 (c) ₹84 (d) ₹252
35. 35.9 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 5 days (d) 6 days
36. 36.If 5 notebooks cost ₹25, how much do 4 notebooks cost? (a) ₹25 (b) ₹20 (c) ₹100 (d) ₹24
37. 37.If 9 mangoes cost ₹162, how much do 8 mangoes cost? (a) ₹144 (b) ₹1296 (c) ₹162 (d) ₹161
38. 38.₹175 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹35 (b) ₹175 (c) ₹140 (d) ₹141
39. 39.₹476 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹170 (b) ₹306 (c) ₹238 (d) ₹34
40. 40.6 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 22 days (c) 21 days (d) 16 days

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