Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 866 · 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 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 12 days (c) 9 days (d) 4 days
2. 2.8 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 8 days (d) 7 days
3. 3.If 8 kites cost ₹56, how much do 7 kites cost? (a) ₹392 (b) ₹56 (c) ₹55 (d) ₹49
4. 4.If 8 notebooks cost ₹152, how much do 6 notebooks cost? (a) ₹133 (b) ₹912 (c) ₹150 (d) ₹114
5. 5.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 28 days (b) 7 days (c) 10 days (d) 18 days
6. 6.₹195 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹150 (b) ₹60 (c) ₹15 (d) ₹135
7. 7.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 44 days (b) 5 days (c) 45 days (d) 17 days
8. 8.If 5 mangoes cost ₹125, how much do 2 mangoes cost? (a) ₹122 (b) ₹75 (c) ₹50 (d) ₹250
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) 21 days (c) 22 days (d) 5 days
10. 10.If 6 notebooks cost ₹48, how much do 11 notebooks cost? (a) ₹528 (b) ₹96 (c) ₹53 (d) ₹88
11. 11.₹188 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹188 (b) ₹141 (c) ₹94 (d) ₹47
12. 12.If 7 pens cost ₹140, how much do 5 pens cost? (a) ₹138 (b) ₹700 (c) ₹100 (d) ₹120
13. 13.9 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 18 days (b) 14 days (c) 19 days (d) 6 days
14. 14.₹87 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹87 (b) ₹29 (c) ₹59 (d) ₹58
15. 15.If 2 kites cost ₹32, how much do 6 kites cost? (a) ₹112 (b) ₹36 (c) ₹192 (d) ₹96
16. 16.If 2 mangoes cost ₹38, how much do 12 mangoes cost? (a) ₹247 (b) ₹456 (c) ₹228 (d) ₹48
17. 17.If 9 pens cost ₹126, how much do 10 pens cost? (a) ₹1260 (b) ₹127 (c) ₹140 (d) ₹154
18. 18.₹143 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹44 (b) ₹11 (c) ₹99 (d) ₹110
19. 19.If 7 pens cost ₹42, how much do 12 pens cost? (a) ₹72 (b) ₹504 (c) ₹78 (d) ₹47
20. 20.₹140 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹56 (b) ₹70 (c) ₹28 (d) ₹84
21. 21.₹369 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹205 (b) ₹246 (c) ₹41 (d) ₹164
22. 22.₹96 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹40 (b) ₹48 (c) ₹56 (d) ₹8
23. 23.If 3 pens cost ₹21, how much do 4 pens cost? (a) ₹22 (b) ₹84 (c) ₹28 (d) ₹35
24. 24.If 2 pens cost ₹46, how much do 7 pens cost? (a) ₹51 (b) ₹161 (c) ₹184 (d) ₹322
25. 25.8 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 60 days (b) 61 days (c) 21 days (d) 9 days
26. 26.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 32 days (b) 17 days (c) 33 days (d) 7 days
27. 27.₹77 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹56 (b) ₹49 (c) ₹28 (d) ₹7
28. 28.₹208 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹78 (b) ₹130 (c) ₹104 (d) ₹26
29. 29.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹12 (b) ₹60 (c) ₹108 (d) ₹84
30. 30.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 41 days (d) 40 days
31. 31.₹253 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹161 (b) ₹138 (c) ₹23 (d) ₹115
32. 32.₹517 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹329 (b) ₹282 (c) ₹47 (d) ₹235
33. 33.If 3 kites cost ₹51, how much do 4 kites cost? (a) ₹52 (b) ₹204 (c) ₹85 (d) ₹68
34. 34.If 8 pens cost ₹200, how much do 6 pens cost? (a) ₹198 (b) ₹150 (c) ₹175 (d) ₹1200
35. 35.₹25 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹15 (b) ₹20 (c) ₹5 (d) ₹10
36. 36.If 4 pens cost ₹12, how much do 10 pens cost? (a) ₹30 (b) ₹18 (c) ₹33 (d) ₹120
37. 37.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 11 days (c) 10 days (d) 8 days
38. 38.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 14 days (d) 5 days
39. 39.8 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 24 days (b) 25 days (c) 14 days (d) 4 days
40. 40.9 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 27 days (c) 28 days (d) 17 days

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