Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 839 · 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. 1.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 6 days (d) 4 days
2. 2.4 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 14 days (b) 12 days (c) 13 days (d) 16 days
3. 3.If 7 pens cost ₹147, how much do 2 pens cost? (a) ₹142 (b) ₹294 (c) ₹63 (d) ₹42
4. 4.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 49 days (b) 19 days (c) 4 days (d) 9 days
5. 5.₹81 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹9 (b) ₹36 (c) ₹54 (d) ₹45
6. 6.If 6 pens cost ₹66, how much do 2 pens cost? (a) ₹62 (b) ₹132 (c) ₹22 (d) ₹33
7. 7.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 15 days (d) 14 days
8. 8.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 8 days (d) 15 days
9. 9.If 3 mangoes cost ₹9, how much do 8 mangoes cost? (a) ₹72 (b) ₹27 (c) ₹24 (d) ₹14
10. 10.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 40 days (d) 41 days
11. 11.If 3 pens cost ₹36, how much do 5 pens cost? (a) ₹72 (b) ₹38 (c) ₹180 (d) ₹60
12. 12.₹170 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹51 (b) ₹17 (c) ₹85 (d) ₹119
13. 13.If 3 mangoes cost ₹21, how much do 10 mangoes cost? (a) ₹77 (b) ₹70 (c) ₹28 (d) ₹210
14. 14.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 45 days (c) 21 days (d) 9 days
15. 15.₹175 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹100 (b) ₹125 (c) ₹25 (d) ₹75
16. 16.If 5 kites cost ₹115, how much do 6 kites cost? (a) ₹116 (b) ₹690 (c) ₹161 (d) ₹138
17. 17.If 6 mangoes cost ₹90, how much do 2 mangoes cost? (a) ₹86 (b) ₹45 (c) ₹30 (d) ₹180
18. 18.If 8 kites cost ₹96, how much do 3 kites cost? (a) ₹48 (b) ₹91 (c) ₹36 (d) ₹288
19. 19.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 10 days (c) 14 days (d) 4 days
20. 20.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 18 days (c) 4 days (d) 5 days
21. 21.If 3 pens cost ₹54, how much do 4 pens cost? (a) ₹55 (b) ₹90 (c) ₹216 (d) ₹72
22. 22.₹297 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹265 (b) ₹297 (c) ₹33 (d) ₹264
23. 23.6 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 10 days (c) 9 days (d) 8 days
24. 24.₹261 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹233 (b) ₹232 (c) ₹29 (d) ₹261
25. 25.₹143 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹52 (b) ₹13 (c) ₹104 (d) ₹91
26. 26.If 7 pens cost ₹70, how much do 8 pens cost? (a) ₹71 (b) ₹80 (c) ₹90 (d) ₹560
27. 27.3 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 11 days (d) 16 days
28. 28.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 11 days
29. 29.₹138 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹69 (b) ₹115 (c) ₹23 (d) ₹138
30. 30.If 2 kites cost ₹46, how much do 8 kites cost? (a) ₹184 (b) ₹52 (c) ₹207 (d) ₹368
31. 31.₹133 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹19 (b) ₹95 (c) ₹38 (d) ₹114
32. 32.₹336 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹96 (b) ₹48 (c) ₹240 (d) ₹168
33. 33.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 16 days (c) 7 days (d) 28 days
34. 34.6 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 6 days (d) 5 days
35. 35.If 5 pens cost ₹105, how much do 8 pens cost? (a) ₹189 (b) ₹108 (c) ₹840 (d) ₹168
36. 36.If 5 notebooks cost ₹20, how much do 2 notebooks cost? (a) ₹12 (b) ₹40 (c) ₹8 (d) ₹17
37. 37.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 6 days (c) 10 days (d) 4 days
38. 38.₹84 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹54 (b) ₹42 (c) ₹30 (d) ₹6
39. 39.₹99 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹44 (b) ₹11 (c) ₹66 (d) ₹55
40. 40.₹215 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹215 (b) ₹43 (c) ₹173 (d) ₹172

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