Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 1 · 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 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 10 days (d) 9 days
2. 2.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 15 days (d) 7 days
3. 3.₹455 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹315 (b) ₹350 (c) ₹140 (d) ₹35
4. 4.₹253 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹207 (b) ₹230 (c) ₹46 (d) ₹23
5. 5.₹344 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹129 (b) ₹43 (c) ₹172 (d) ₹215
6. 6.If 8 mangoes cost ₹48, how much do 4 mangoes cost? (a) ₹44 (b) ₹30 (c) ₹24 (d) ₹192
7. 7.₹18 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹9 (b) ₹18 (c) ₹6 (d) ₹12
8. 8.If 5 pens cost ₹65, how much do 3 pens cost? (a) ₹63 (b) ₹195 (c) ₹39 (d) ₹52
9. 9.₹90 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹80 (b) ₹45 (c) ₹10 (d) ₹90
10. 10.₹144 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹84 (b) ₹60 (c) ₹72 (d) ₹12
11. 11.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 20 days (c) 5 days (d) 11 days
12. 12.₹205 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹41 (b) ₹165 (c) ₹164 (d) ₹205
13. 13.6 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 14 days (b) 8 days (c) 18 days (d) 10 days
14. 14.₹45 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹35 (b) ₹40 (c) ₹10 (d) ₹5
15. 15.If 3 pens cost ₹69, how much do 7 pens cost? (a) ₹161 (b) ₹483 (c) ₹73 (d) ₹184
16. 16.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 14 days (d) 5 days
17. 17.If 3 pens cost ₹66, how much do 2 pens cost? (a) ₹66 (b) ₹132 (c) ₹44 (d) ₹65
18. 18.3 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 5 days (d) 16 days
19. 19.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 8 days (c) 57 days (d) 56 days
20. 20.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 9 days (d) 1 day
21. 21.₹238 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹85 (b) ₹153 (c) ₹119 (d) ₹17
22. 22.If 9 kites cost ₹45, how much do 10 kites cost? (a) ₹46 (b) ₹450 (c) ₹55 (d) ₹50
23. 23.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 7 days (d) 6 days
24. 24.₹160 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹80 (b) ₹160 (c) ₹128 (d) ₹32
25. 25.If 8 pens cost ₹144, how much do 11 pens cost? (a) ₹198 (b) ₹147 (c) ₹1584 (d) ₹216
26. 26.₹258 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹258 (b) ₹129 (c) ₹43 (d) ₹215
27. 27.If 6 mangoes cost ₹126, how much do 5 mangoes cost? (a) ₹630 (b) ₹105 (c) ₹125 (d) ₹126
28. 28.₹350 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹175 (b) ₹250 (c) ₹50 (d) ₹100
29. 29.If 7 kites cost ₹21, how much do 8 kites cost? (a) ₹168 (b) ₹27 (c) ₹22 (d) ₹24
30. 30.₹208 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹128 (b) ₹80 (c) ₹16 (d) ₹104
31. 31.If 6 kites cost ₹144, how much do 12 kites cost? (a) ₹288 (b) ₹312 (c) ₹1728 (d) ₹150
32. 32.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 2 days (c) 18 days (d) 12 days
33. 33.₹602 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹301 (b) ₹387 (c) ₹43 (d) ₹215
34. 34.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 10 days (d) 13 days
35. 35.₹290 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹29 (b) ₹290 (c) ₹261 (d) ₹145
36. 36.If 9 mangoes cost ₹63, how much do 11 mangoes cost? (a) ₹693 (b) ₹77 (c) ₹84 (d) ₹65
37. 37.₹225 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹200 (b) ₹50 (c) ₹175 (d) ₹25
38. 38.If 6 notebooks cost ₹18, how much do 11 notebooks cost? (a) ₹23 (b) ₹198 (c) ₹33 (d) ₹36
39. 39.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 1 day (d) 16 days
40. 40.9 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 10 days (d) 11 days

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