Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 620 · 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.₹121 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹88 (b) ₹11 (c) ₹33 (d) ₹99
2. 2.₹320 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹32 (b) ₹96 (c) ₹160 (d) ₹224
3. 3.₹70 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹14 (b) ₹28 (c) ₹42 (d) ₹35
4. 4.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 26 days (c) 11 days (d) 15 days
5. 5.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 26 days (d) 27 days
6. 6.If 4 mangoes cost ₹96, how much do 5 mangoes cost? (a) ₹97 (b) ₹144 (c) ₹480 (d) ₹120
7. 7.If 6 notebooks cost ₹30, how much do 8 notebooks cost? (a) ₹45 (b) ₹40 (c) ₹240 (d) ₹32
8. 8.₹87 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹87 (b) ₹29 (c) ₹58 (d) ₹59
9. 9.If 8 pens cost ₹176, how much do 9 pens cost? (a) ₹198 (b) ₹220 (c) ₹1584 (d) ₹177
10. 10.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 48 days (c) 6 days (d) 3 days
11. 11.If 7 pens cost ₹147, how much do 11 pens cost? (a) ₹231 (b) ₹1617 (c) ₹151 (d) ₹252
12. 12.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 13 days (d) 12 days
13. 13.If 3 mangoes cost ₹63, how much do 8 mangoes cost? (a) ₹168 (b) ₹68 (c) ₹189 (d) ₹504
14. 14.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 14 days (c) 15 days (d) 2 days
15. 15.If 4 notebooks cost ₹12, how much do 8 notebooks cost? (a) ₹24 (b) ₹27 (c) ₹96 (d) ₹16
16. 16.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 3 days (c) 12 days (d) 11 days
17. 17.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 18 days (b) 28 days (c) 7 days (d) 10 days
18. 18.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 7 days (c) 40 days (d) 19 days
19. 19.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 1 day (c) 2 days (d) 13 days
20. 20.If 8 mangoes cost ₹128, how much do 2 mangoes cost? (a) ₹256 (b) ₹48 (c) ₹32 (d) ₹122
21. 21.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 18 days (c) 10 days (d) 6 days
22. 22.₹90 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹90 (b) ₹45 (c) ₹80 (d) ₹10
23. 23.₹288 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹128 (b) ₹144 (c) ₹32 (d) ₹160
24. 24.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 7 days
25. 25.If 7 mangoes cost ₹21, how much do 8 mangoes cost? (a) ₹24 (b) ₹22 (c) ₹168 (d) ₹27
26. 26.If 3 mangoes cost ₹27, how much do 12 mangoes cost? (a) ₹324 (b) ₹36 (c) ₹108 (d) ₹117
27. 27.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 11 days (d) 4 days
28. 28.If 3 pens cost ₹60, how much do 2 pens cost? (a) ₹120 (b) ₹59 (c) ₹60 (d) ₹40
29. 29.₹112 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹8 (b) ₹56 (c) ₹72 (d) ₹40
30. 30.If 5 notebooks cost ₹105, how much do 2 notebooks cost? (a) ₹210 (b) ₹42 (c) ₹63 (d) ₹102
31. 31.If 8 kites cost ₹168, how much do 9 kites cost? (a) ₹189 (b) ₹169 (c) ₹210 (d) ₹1512
32. 32.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 12 days (c) 4 days (d) 2 days
33. 33.If 9 mangoes cost ₹72, how much do 10 mangoes cost? (a) ₹73 (b) ₹88 (c) ₹720 (d) ₹80
34. 34.₹507 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹390 (b) ₹39 (c) ₹156 (d) ₹351
35. 35.If 4 notebooks cost ₹60, how much do 8 notebooks cost? (a) ₹480 (b) ₹135 (c) ₹64 (d) ₹120
36. 36.If 8 pens cost ₹56, how much do 10 pens cost? (a) ₹70 (b) ₹560 (c) ₹77 (d) ₹58
37. 37.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 11 days (c) 2 days (d) 10 days
38. 38.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 9 days (d) 17 days
39. 39.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 4 days (d) 3 days
40. 40.If 5 mangoes cost ₹95, how much do 7 mangoes cost? (a) ₹97 (b) ₹665 (c) ₹152 (d) ₹133

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