Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 385 · 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 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 3 days (c) 27 days (d) 15 days
2. 2.6 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 18 days (c) 24 days (d) 6 days
3. 3.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 28 days (d) 7 days
4. 4.If 6 notebooks cost ₹78, how much do 3 notebooks cost? (a) ₹39 (b) ₹52 (c) ₹234 (d) ₹75
5. 5.If 6 notebooks cost ₹30, how much do 7 notebooks cost? (a) ₹31 (b) ₹40 (c) ₹35 (d) ₹210
6. 6.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 2 days (d) 8 days
7. 7.₹70 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹10 (b) ₹70 (c) ₹60 (d) ₹35
8. 8.₹135 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹120 (b) ₹135 (c) ₹15 (d) ₹121
9. 9.If 3 pens cost ₹12, how much do 4 pens cost? (a) ₹48 (b) ₹20 (c) ₹16 (d) ₹13
10. 10.₹140 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹140 (b) ₹20 (c) ₹120 (d) ₹70
11. 11.If 5 notebooks cost ₹85, how much do 3 notebooks cost? (a) ₹255 (b) ₹68 (c) ₹83 (d) ₹51
12. 12.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 11 days (d) 12 days
13. 13.If 6 mangoes cost ₹42, how much do 3 mangoes cost? (a) ₹28 (b) ₹126 (c) ₹39 (d) ₹21
14. 14.If 7 kites cost ₹49, how much do 8 kites cost? (a) ₹63 (b) ₹392 (c) ₹56 (d) ₹50
15. 15.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 41 days (c) 40 days (d) 16 days
16. 16.If 7 notebooks cost ₹98, how much do 6 notebooks cost? (a) ₹98 (b) ₹588 (c) ₹84 (d) ₹97
17. 17.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹60 (b) ₹108 (c) ₹84 (d) ₹12
18. 18.₹253 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹46 (b) ₹23 (c) ₹230 (d) ₹207
19. 19.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 5 days (c) 45 days (d) 9 days
20. 20.If 9 mangoes cost ₹189, how much do 11 mangoes cost? (a) ₹252 (b) ₹231 (c) ₹191 (d) ₹2079
21. 21.₹198 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹99 (b) ₹33 (c) ₹198 (d) ₹165
22. 22.6 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) 6 days (d) 5 days
23. 23.₹87 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹87 (b) ₹59 (c) ₹29 (d) ₹58
24. 24.If 4 kites cost ₹68, how much do 8 kites cost? (a) ₹136 (b) ₹72 (c) ₹544 (d) ₹153
25. 25.If 4 pens cost ₹68, how much do 12 pens cost? (a) ₹76 (b) ₹816 (c) ₹221 (d) ₹204
26. 26.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 13 days (c) 5 days (d) 3 days
27. 27.₹162 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹126 (b) ₹36 (c) ₹18 (d) ₹81
28. 28.₹550 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹400 (b) ₹50 (c) ₹275 (d) ₹150
29. 29.If 5 mangoes cost ₹25, how much do 12 mangoes cost? (a) ₹32 (b) ₹300 (c) ₹60 (d) ₹65
30. 30.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 2 days (d) 3 days
31. 31.If 4 kites cost ₹88, how much do 12 kites cost? (a) ₹1056 (b) ₹264 (c) ₹96 (d) ₹286
32. 32.If 9 pens cost ₹162, how much do 3 pens cost? (a) ₹156 (b) ₹54 (c) ₹486 (d) ₹72
33. 33.₹130 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹91 (b) ₹65 (c) ₹13 (d) ₹39
34. 34.If 8 notebooks cost ₹136, how much do 3 notebooks cost? (a) ₹68 (b) ₹51 (c) ₹131 (d) ₹408
35. 35.If 4 mangoes cost ₹12, how much do 5 mangoes cost? (a) ₹15 (b) ₹13 (c) ₹60 (d) ₹18
36. 36.₹240 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹120 (b) ₹216 (c) ₹240 (d) ₹24
37. 37.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 17 days (c) 5 days (d) 44 days
38. 38.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 11 days (d) 16 days
39. 39.If 8 pens cost ₹176, how much do 9 pens cost? (a) ₹177 (b) ₹220 (c) ₹198 (d) ₹1584
40. 40.₹100 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹100 (b) ₹25 (c) ₹50 (d) ₹75

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