Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 480 · 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. 1.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 5 days (d) 8 days
2. 2.6 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 13 days (b) 10 days (c) 12 days (d) 6 days
3. 3.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 15 days (d) 20 days
4. 4.6 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 6 days (c) 4 days (d) 2 days
5. 5.If 7 notebooks cost ₹140, how much do 4 notebooks cost? (a) ₹80 (b) ₹560 (c) ₹137 (d) ₹100
6. 6.6 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 3 days (c) 12 days (d) 9 days
7. 7.₹272 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹34 (b) ₹238 (c) ₹136 (d) ₹272
8. 8.₹156 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹12 (b) ₹48 (c) ₹78 (d) ₹108
9. 9.₹145 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹29 (b) ₹87 (c) ₹116 (d) ₹58
10. 10.If 2 pens cost ₹14, how much do 3 pens cost? (a) ₹21 (b) ₹42 (c) ₹28 (d) ₹15
11. 11.₹120 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹60 (b) ₹36 (c) ₹12 (d) ₹84
12. 12.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 2 days (c) 3 days (d) 4 days
13. 13.If 2 mangoes cost ₹18, how much do 4 mangoes cost? (a) ₹45 (b) ₹36 (c) ₹20 (d) ₹72
14. 14.If 9 kites cost ₹180, how much do 7 kites cost? (a) ₹160 (b) ₹140 (c) ₹1260 (d) ₹178
15. 15.If 6 kites cost ₹24, how much do 5 kites cost? (a) ₹23 (b) ₹24 (c) ₹120 (d) ₹20
16. 16.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 2 days (d) 7 days
17. 17.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 6 days (c) 4 days (d) 5 days
18. 18.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 5 days (d) 9 days
19. 19.If 7 notebooks cost ₹126, how much do 12 notebooks cost? (a) ₹131 (b) ₹1512 (c) ₹216 (d) ₹234
20. 20.If 4 pens cost ₹48, how much do 6 pens cost? (a) ₹84 (b) ₹288 (c) ₹72 (d) ₹50
21. 21.If 2 pens cost ₹34, how much do 6 pens cost? (a) ₹38 (b) ₹102 (c) ₹119 (d) ₹204
22. 22.If 9 mangoes cost ₹54, how much do 11 mangoes cost? (a) ₹66 (b) ₹56 (c) ₹594 (d) ₹72
23. 23.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 2 days (d) 3 days
24. 24.If 7 kites cost ₹35, how much do 11 kites cost? (a) ₹39 (b) ₹60 (c) ₹385 (d) ₹55
25. 25.₹546 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹351 (b) ₹39 (c) ₹195 (d) ₹273
26. 26.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 1 day (d) 11 days
27. 27.₹385 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹70 (b) ₹350 (c) ₹315 (d) ₹35
28. 28.₹220 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹60 (b) ₹20 (c) ₹160 (d) ₹110
29. 29.If 9 pens cost ₹117, how much do 12 pens cost? (a) ₹169 (b) ₹156 (c) ₹1404 (d) ₹120
30. 30.5 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 10 days (c) 9 days (d) 11 days
31. 31.₹90 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹30 (b) ₹45 (c) ₹60 (d) ₹90
32. 32.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 11 days (d) 10 days
33. 33.If 3 pens cost ₹66, how much do 8 pens cost? (a) ₹528 (b) ₹71 (c) ₹198 (d) ₹176
34. 34.If 4 kites cost ₹68, how much do 11 kites cost? (a) ₹748 (b) ₹187 (c) ₹204 (d) ₹75
35. 35.₹400 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹250 (b) ₹200 (c) ₹150 (d) ₹50
36. 36.₹299 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹115 (b) ₹23 (c) ₹184 (d) ₹207
37. 37.₹168 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹168 (b) ₹147 (c) ₹21 (d) ₹84
38. 38.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 29 days (b) 28 days (c) 13 days (d) 1 day
39. 39.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 25 days (d) 13 days
40. 40.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 17 days

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