Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 594 · 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.If 9 notebooks cost ₹27, how much do 11 notebooks cost? (a) ₹36 (b) ₹29 (c) ₹297 (d) ₹33
2. 2.If 5 kites cost ₹105, how much do 10 kites cost? (a) ₹1050 (b) ₹210 (c) ₹110 (d) ₹231
3. 3.₹160 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹20 (b) ₹80 (c) ₹60 (d) ₹100
4. 4.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 22 days (c) 14 days (d) 23 days
5. 5.If 7 notebooks cost ₹49, how much do 11 notebooks cost? (a) ₹53 (b) ₹84 (c) ₹77 (d) ₹539
6. 6.If 2 mangoes cost ₹34, how much do 4 mangoes cost? (a) ₹85 (b) ₹68 (c) ₹36 (d) ₹136
7. 7.If 8 notebooks cost ₹200, how much do 5 notebooks cost? (a) ₹197 (b) ₹1000 (c) ₹125 (d) ₹150
8. 8.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 8 days (d) 1 day
9. 9.₹65 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹52 (b) ₹65 (c) ₹13 (d) ₹53
10. 10.If 7 notebooks cost ₹42, how much do 8 notebooks cost? (a) ₹43 (b) ₹48 (c) ₹54 (d) ₹336
11. 11.9 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) 15 days (d) 27 days
12. 12.₹451 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹328 (b) ₹369 (c) ₹41 (d) ₹123
13. 13.₹70 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹50 (b) ₹20 (c) ₹10 (d) ₹35
14. 14.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 19 days (c) 10 days (d) 18 days
15. 15.If 2 mangoes cost ₹48, how much do 4 mangoes cost? (a) ₹50 (b) ₹120 (c) ₹192 (d) ₹96
16. 16.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 15 days (c) 7 days (d) 8 days
17. 17.3 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
18. 18.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 11 days (c) 15 days (d) 26 days
19. 19.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 14 days (c) 13 days (d) 15 days
20. 20.₹126 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹108 (b) ₹126 (c) ₹63 (d) ₹18
21. 21.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 5 days (d) 45 days
22. 22.If 3 pens cost ₹57, how much do 9 pens cost? (a) ₹190 (b) ₹513 (c) ₹171 (d) ₹63
23. 23.If 5 notebooks cost ₹45, how much do 6 notebooks cost? (a) ₹270 (b) ₹46 (c) ₹54 (d) ₹63
24. 24.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 18 days (c) 19 days (d) 6 days
25. 25.If 3 pens cost ₹45, how much do 4 pens cost? (a) ₹180 (b) ₹46 (c) ₹60 (d) ₹75
26. 26.₹120 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹120 (b) ₹60 (c) ₹30 (d) ₹90
27. 27.If 4 kites cost ₹48, how much do 12 kites cost? (a) ₹576 (b) ₹56 (c) ₹144 (d) ₹156
28. 28.If 7 notebooks cost ₹140, how much do 8 notebooks cost? (a) ₹180 (b) ₹160 (c) ₹1120 (d) ₹141
29. 29.₹45 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹41 (b) ₹5 (c) ₹45 (d) ₹40
30. 30.₹25 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹20 (b) ₹15 (c) ₹10 (d) ₹5
31. 31.₹384 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹224 (b) ₹32 (c) ₹192 (d) ₹160
32. 32.₹319 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹29 (b) ₹232 (c) ₹87 (d) ₹261
33. 33.If 7 kites cost ₹175, how much do 12 kites cost? (a) ₹180 (b) ₹2100 (c) ₹300 (d) ₹325
34. 34.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 2 days (c) 8 days (d) 11 days
35. 35.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 3 days (d) 4 days
36. 36.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 26 days (c) 10 days (d) 16 days
37. 37.If 5 kites cost ₹85, how much do 3 kites cost? (a) ₹83 (b) ₹51 (c) ₹68 (d) ₹255
38. 38.If 6 mangoes cost ₹120, how much do 7 mangoes cost? (a) ₹840 (b) ₹140 (c) ₹160 (d) ₹121
39. 39.If 5 pens cost ₹65, how much do 3 pens cost? (a) ₹195 (b) ₹39 (c) ₹52 (d) ₹63
40. 40.4 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 13 days (c) 8 days (d) 10 days

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