Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 330 · 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 11 days. How many days will 11 workers take, working at the same speed? (a) 10 days (b) 13 days (c) 8 days (d) 9 days
2. 2.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 8 days (d) 3 days
3. 3.If 3 mangoes cost ₹48, how much do 4 mangoes cost? (a) ₹80 (b) ₹192 (c) ₹49 (d) ₹64
4. 4.₹136 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹136 (b) ₹102 (c) ₹68 (d) ₹34
5. 5.If 3 mangoes cost ₹27, how much do 5 mangoes cost? (a) ₹29 (b) ₹45 (c) ₹54 (d) ₹135
6. 6.If 9 kites cost ₹153, how much do 6 kites cost? (a) ₹102 (b) ₹150 (c) ₹119 (d) ₹918
7. 7.If 2 notebooks cost ₹48, how much do 10 notebooks cost? (a) ₹480 (b) ₹240 (c) ₹264 (d) ₹56
8. 8.If 9 mangoes cost ₹81, how much do 10 mangoes cost? (a) ₹810 (b) ₹90 (c) ₹82 (d) ₹99
9. 9.₹110 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹10 (b) ₹70 (c) ₹55 (d) ₹40
10. 10.If 5 pens cost ₹85, how much do 7 pens cost? (a) ₹119 (b) ₹87 (c) ₹136 (d) ₹595
11. 11.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 21 days (d) 7 days
12. 12.₹135 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹108 (b) ₹27 (c) ₹54 (d) ₹81
13. 13.If 6 kites cost ₹108, how much do 11 kites cost? (a) ₹1188 (b) ₹113 (c) ₹216 (d) ₹198
14. 14.₹192 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹96 (b) ₹24 (c) ₹72 (d) ₹120
15. 15.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 8 days (c) 9 days (d) 7 days
16. 16.If 2 notebooks cost ₹16, how much do 3 notebooks cost? (a) ₹48 (b) ₹17 (c) ₹24 (d) ₹32
17. 17.₹330 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹180 (b) ₹150 (c) ₹165 (d) ₹30
18. 18.₹35 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹30 (b) ₹10 (c) ₹25 (d) ₹5
19. 19.If 2 kites cost ₹12, how much do 9 kites cost? (a) ₹19 (b) ₹60 (c) ₹54 (d) ₹108
20. 20.If 6 kites cost ₹90, how much do 2 kites cost? (a) ₹30 (b) ₹86 (c) ₹45 (d) ₹180
21. 21.If 3 pens cost ₹72, how much do 11 pens cost? (a) ₹792 (b) ₹80 (c) ₹264 (d) ₹288
22. 22.If 9 kites cost ₹36, how much do 10 kites cost? (a) ₹360 (b) ₹37 (c) ₹40 (d) ₹44
23. 23.If 6 pens cost ₹138, how much do 12 pens cost? (a) ₹299 (b) ₹276 (c) ₹1656 (d) ₹144
24. 24.₹99 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹66 (b) ₹11 (c) ₹55 (d) ₹44
25. 25.If 8 notebooks cost ₹48, how much do 2 notebooks cost? (a) ₹42 (b) ₹18 (c) ₹96 (d) ₹12
26. 26.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 9 days (d) 8 days
27. 27.₹129 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹43 (b) ₹129 (c) ₹87 (d) ₹86
28. 28.₹616 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹44 (b) ₹396 (c) ₹308 (d) ₹220
29. 29.9 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 24 days (c) 25 days (d) 2 days
30. 30.If 9 kites cost ₹225, how much do 7 kites cost? (a) ₹200 (b) ₹1575 (c) ₹223 (d) ₹175
31. 31.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 4 days (d) 7 days
32. 32.If 7 notebooks cost ₹63, how much do 2 notebooks cost? (a) ₹126 (b) ₹58 (c) ₹27 (d) ₹18
33. 33.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 24 days (b) 10 days (c) 6 days (d) 14 days
34. 34.If 2 kites cost ₹6, how much do 6 kites cost? (a) ₹10 (b) ₹21 (c) ₹36 (d) ₹18
35. 35.If 8 notebooks cost ₹88, how much do 7 notebooks cost? (a) ₹87 (b) ₹88 (c) ₹77 (d) ₹616
36. 36.₹70 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹10 (b) ₹30 (c) ₹35 (d) ₹40
37. 37.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 14 days (c) 5 days (d) 3 days
38. 38.₹441 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹49 (b) ₹393 (c) ₹441 (d) ₹392
39. 39.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 27 days (d) 3 days
40. 40.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 37 days (c) 15 days (d) 36 days

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