Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 991 · 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. 1.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 28 days (c) 27 days (d) 13 days
2. 2.₹533 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹369 (b) ₹41 (c) ₹164 (d) ₹410
3. 3.If 5 notebooks cost ₹120, how much do 9 notebooks cost? (a) ₹1080 (b) ₹124 (c) ₹240 (d) ₹216
4. 4.₹132 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹66 (b) ₹22 (c) ₹110 (d) ₹132
5. 5.₹126 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹126 (b) ₹84 (c) ₹63 (d) ₹42
6. 6.If 9 pens cost ₹216, how much do 6 pens cost? (a) ₹213 (b) ₹1296 (c) ₹168 (d) ₹144
7. 7.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 9 days (d) 8 days
8. 8.₹55 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹5 (b) ₹20 (c) ₹35 (d) ₹40
9. 9.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 22 days (d) 21 days
10. 10.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 3 days (c) 4 days (d) 12 days
11. 11.If 8 pens cost ₹80, how much do 6 pens cost? (a) ₹60 (b) ₹70 (c) ₹78 (d) ₹480
12. 12.₹150 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹150 (b) ₹125 (c) ₹25 (d) ₹75
13. 13.₹273 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹234 (b) ₹39 (c) ₹195 (d) ₹78
14. 14.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 16 days (d) 17 days
15. 15.₹333 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹333 (b) ₹297 (c) ₹296 (d) ₹37
16. 16.If 3 kites cost ₹60, how much do 2 kites cost? (a) ₹120 (b) ₹59 (c) ₹60 (d) ₹40
17. 17.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 29 days (b) 28 days (c) 1 day (d) 13 days
18. 18.8 workers can build a wall in 15 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 31 days (c) 19 days (d) 30 days
19. 19.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 8 days (d) 7 days
20. 20.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 21 days (c) 22 days (d) 3 days
21. 21.₹266 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹114 (b) ₹133 (c) ₹152 (d) ₹38
22. 22.₹65 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹25 (b) ₹40 (c) ₹5 (d) ₹45
23. 23.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 43 days (b) 18 days (c) 42 days (d) 10 days
24. 24.If 7 pens cost ₹21, how much do 8 pens cost? (a) ₹168 (b) ₹24 (c) ₹22 (d) ₹27
25. 25.If 8 mangoes cost ₹72, how much do 5 mangoes cost? (a) ₹54 (b) ₹45 (c) ₹69 (d) ₹360
26. 26.₹207 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹46 (b) ₹23 (c) ₹184 (d) ₹161
27. 27.₹324 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹162 (b) ₹36 (c) ₹252 (d) ₹72
28. 28.If 9 pens cost ₹189, how much do 4 pens cost? (a) ₹84 (b) ₹184 (c) ₹756 (d) ₹105
29. 29.₹360 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹36 (b) ₹180 (c) ₹324 (d) ₹360
30. 30.₹387 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹86 (b) ₹344 (c) ₹301 (d) ₹43
31. 31.If 5 mangoes cost ₹90, how much do 11 mangoes cost? (a) ₹990 (b) ₹216 (c) ₹198 (d) ₹96
32. 32.₹260 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹20 (b) ₹180 (c) ₹80 (d) ₹130
33. 33.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 15 days (c) 14 days (d) 9 days
34. 34.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 1 day (c) 3 days (d) 9 days
35. 35.If 6 pens cost ₹54, how much do 2 pens cost? (a) ₹18 (b) ₹50 (c) ₹27 (d) ₹108
36. 36.₹143 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹91 (b) ₹13 (c) ₹52 (d) ₹104
37. 37.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 25 days (d) 9 days
38. 38.If 5 pens cost ₹100, how much do 11 pens cost? (a) ₹106 (b) ₹240 (c) ₹1100 (d) ₹220
39. 39.₹312 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹24 (b) ₹192 (c) ₹120 (d) ₹156
40. 40.8 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 16 days (c) 24 days (d) 8 days

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