Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 229 · 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 12 days. How many days will 4 workers take, working at the same speed? (a) 28 days (b) 7 days (c) 27 days (d) 17 days
2. 2.If 2 pens cost ₹26, how much do 6 pens cost? (a) ₹78 (b) ₹156 (c) ₹91 (d) ₹30
3. 3.If 6 kites cost ₹150, how much do 12 kites cost? (a) ₹1800 (b) ₹300 (c) ₹156 (d) ₹325
4. 4.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 27 days (c) 15 days (d) 26 days
5. 5.If 4 notebooks cost ₹40, how much do 9 notebooks cost? (a) ₹360 (b) ₹100 (c) ₹90 (d) ₹45
6. 6.If 2 kites cost ₹30, how much do 3 kites cost? (a) ₹31 (b) ₹45 (c) ₹60 (d) ₹90
7. 7.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 6 days (d) 7 days
8. 8.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 10 days (c) 16 days (d) 1 day
9. 9.If 2 mangoes cost ₹40, how much do 7 mangoes cost? (a) ₹140 (b) ₹45 (c) ₹160 (d) ₹280
10. 10.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 17 days (d) 2 days
11. 11.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 4 days (d) 5 days
12. 12.₹88 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹11 (b) ₹88 (c) ₹44 (d) ₹77
13. 13.If 9 mangoes cost ₹198, how much do 5 mangoes cost? (a) ₹990 (b) ₹132 (c) ₹110 (d) ₹194
14. 14.₹120 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹15 (b) ₹60 (c) ₹105 (d) ₹120
15. 15.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 14 days (c) 4 days (d) 15 days
16. 16.₹260 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹130 (b) ₹180 (c) ₹20 (d) ₹80
17. 17.If 4 mangoes cost ₹16, how much do 3 mangoes cost? (a) ₹16 (b) ₹12 (c) ₹48 (d) ₹15
18. 18.If 4 mangoes cost ₹16, how much do 5 mangoes cost? (a) ₹17 (b) ₹80 (c) ₹24 (d) ₹20
19. 19.If 5 kites cost ₹25, how much do 10 kites cost? (a) ₹250 (b) ₹55 (c) ₹30 (d) ₹50
20. 20.If 4 notebooks cost ₹20, how much do 12 notebooks cost? (a) ₹240 (b) ₹65 (c) ₹28 (d) ₹60
21. 21.₹429 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹273 (b) ₹39 (c) ₹156 (d) ₹312
22. 22.If 7 notebooks cost ₹126, how much do 9 notebooks cost? (a) ₹1134 (b) ₹180 (c) ₹162 (d) ₹128
23. 23.If 4 pens cost ₹88, how much do 7 pens cost? (a) ₹91 (b) ₹176 (c) ₹616 (d) ₹154
24. 24.₹276 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹276 (b) ₹46 (c) ₹138 (d) ₹230
25. 25.If 4 notebooks cost ₹36, how much do 9 notebooks cost? (a) ₹324 (b) ₹81 (c) ₹90 (d) ₹41
26. 26.8 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 9 days (c) 8 days (d) 7 days
27. 27.If 8 mangoes cost ₹96, how much do 12 mangoes cost? (a) ₹144 (b) ₹100 (c) ₹1152 (d) ₹156
28. 28.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 15 days (b) 6 days (c) 5 days (d) 20 days
29. 29.9 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 24 days (b) 25 days (c) 14 days (d) 2 days
30. 30.6 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 28 days (d) 17 days
31. 31.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 5 days (d) 13 days
32. 32.₹630 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹405 (b) ₹225 (c) ₹45 (d) ₹315
33. 33.₹297 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹27 (b) ₹54 (c) ₹270 (d) ₹243
34. 34.₹396 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹198 (b) ₹36 (c) ₹72 (d) ₹324
35. 35.₹98 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹7 (b) ₹63 (c) ₹49 (d) ₹35
36. 36.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 12 days (c) 6 days (d) 18 days
37. 37.₹91 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹63 (b) ₹7 (c) ₹28 (d) ₹70
38. 38.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 3 days (c) 2 days (d) 18 days
39. 39.₹140 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹50 (b) ₹70 (c) ₹90 (d) ₹10
40. 40.If 3 kites cost ₹33, how much do 6 kites cost? (a) ₹66 (b) ₹36 (c) ₹77 (d) ₹198

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