Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 109 · 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.₹176 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹66 (b) ₹88 (c) ₹110 (d) ₹22
2. 2.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 4 days (d) 27 days
3. 3.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 19 days (c) 12 days (d) 18 days
4. 4.If 9 notebooks cost ₹144, how much do 8 notebooks cost? (a) ₹143 (b) ₹144 (c) ₹128 (d) ₹1152
5. 5.9 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 16 days (d) 10 days
6. 6.₹192 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹16 (b) ₹96 (c) ₹80 (d) ₹112
7. 7.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 25 days (c) 23 days (d) 24 days
8. 8.₹143 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹99 (b) ₹88 (c) ₹55 (d) ₹11
9. 9.If 9 kites cost ₹180, how much do 2 kites cost? (a) ₹360 (b) ₹60 (c) ₹173 (d) ₹40
10. 10.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 43 days (c) 42 days (d) 20 days
11. 11.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 28 days (b) 11 days (c) 17 days (d) 7 days
12. 12.If 6 pens cost ₹150, how much do 9 pens cost? (a) ₹153 (b) ₹1350 (c) ₹250 (d) ₹225
13. 13.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 11 days (c) 16 days (d) 15 days
14. 14.If 2 mangoes cost ₹30, how much do 12 mangoes cost? (a) ₹195 (b) ₹180 (c) ₹40 (d) ₹360
15. 15.₹377 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹29 (b) ₹145 (c) ₹261 (d) ₹232
16. 16.If 8 kites cost ₹48, how much do 5 kites cost? (a) ₹36 (b) ₹45 (c) ₹30 (d) ₹240
17. 17.If 8 mangoes cost ₹104, how much do 5 mangoes cost? (a) ₹101 (b) ₹520 (c) ₹78 (d) ₹65
18. 18.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 20 days (c) 5 days (d) 14 days
19. 19.₹440 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹240 (b) ₹220 (c) ₹200 (d) ₹40
20. 20.If 6 kites cost ₹30, how much do 4 kites cost? (a) ₹120 (b) ₹20 (c) ₹25 (d) ₹28
21. 21.₹242 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹121 (b) ₹22 (c) ₹198 (d) ₹44
22. 22.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 19 days (c) 2 days (d) 4 days
23. 23.If 4 mangoes cost ₹80, how much do 7 mangoes cost? (a) ₹160 (b) ₹560 (c) ₹140 (d) ₹83
24. 24.₹280 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹160 (b) ₹140 (c) ₹40 (d) ₹120
25. 25.If 6 pens cost ₹120, how much do 9 pens cost? (a) ₹1080 (b) ₹200 (c) ₹180 (d) ₹123
26. 26.₹112 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹56 (b) ₹70 (c) ₹42 (d) ₹14
27. 27.8 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 61 days (b) 60 days (c) 9 days (d) 21 days
28. 28.₹165 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹15 (b) ₹105 (c) ₹75 (d) ₹90
29. 29.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 32 days (c) 33 days (d) 2 days
30. 30.If 6 kites cost ₹132, how much do 4 kites cost? (a) ₹528 (b) ₹130 (c) ₹110 (d) ₹88
31. 31.₹117 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹72 (b) ₹9 (c) ₹45 (d) ₹81
32. 32.If 8 notebooks cost ₹112, how much do 10 notebooks cost? (a) ₹154 (b) ₹140 (c) ₹114 (d) ₹1120
33. 33.₹552 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹230 (b) ₹276 (c) ₹322 (d) ₹46
34. 34.If 6 kites cost ₹108, how much do 11 kites cost? (a) ₹198 (b) ₹113 (c) ₹216 (d) ₹1188
35. 35.If 6 pens cost ₹54, how much do 5 pens cost? (a) ₹53 (b) ₹270 (c) ₹45 (d) ₹54
36. 36.₹429 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹195 (b) ₹39 (c) ₹273 (d) ₹234
37. 37.If 4 mangoes cost ₹72, how much do 12 mangoes cost? (a) ₹864 (b) ₹80 (c) ₹234 (d) ₹216
38. 38.If 4 kites cost ₹28, how much do 6 kites cost? (a) ₹30 (b) ₹49 (c) ₹168 (d) ₹42
39. 39.If 5 notebooks cost ₹35, how much do 12 notebooks cost? (a) ₹91 (b) ₹420 (c) ₹84 (d) ₹42
40. 40.₹44 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹22 (b) ₹44 (c) ₹33 (d) ₹11

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