Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 26 · 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 mangoes cost ₹207, how much do 4 mangoes cost? (a) ₹202 (b) ₹92 (c) ₹115 (d) ₹828
2. 2.If 7 notebooks cost ₹42, how much do 4 notebooks cost? (a) ₹39 (b) ₹30 (c) ₹24 (d) ₹168
3. 3.₹462 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹231 (b) ₹42 (c) ₹378 (d) ₹84
4. 4.8 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 25 days (b) 24 days (c) 14 days (d) 4 days
5. 5.If 6 pens cost ₹36, how much do 7 pens cost? (a) ₹252 (b) ₹42 (c) ₹48 (d) ₹37
6. 6.₹104 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹8 (b) ₹40 (c) ₹52 (d) ₹64
7. 7.₹75 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹15 (b) ₹30 (c) ₹60 (d) ₹45
8. 8.4 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 10 days (c) 8 days (d) 13 days
9. 9.₹220 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹20 (b) ₹180 (c) ₹40 (d) ₹110
10. 10.If 2 pens cost ₹32, how much do 4 pens cost? (a) ₹34 (b) ₹128 (c) ₹64 (d) ₹80
11. 11.₹624 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹312 (b) ₹48 (c) ₹240 (d) ₹384
12. 12.₹88 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹72 (b) ₹44 (c) ₹16 (d) ₹8
13. 13.If 4 mangoes cost ₹56, how much do 10 mangoes cost? (a) ₹140 (b) ₹154 (c) ₹62 (d) ₹560
14. 14.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 4 days (d) 19 days
15. 15.If 4 kites cost ₹20, how much do 6 kites cost? (a) ₹30 (b) ₹35 (c) ₹120 (d) ₹22
16. 16.₹117 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹72 (b) ₹81 (c) ₹45 (d) ₹9
17. 17.7 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
18. 18.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 15 days (c) 10 days (d) 14 days
19. 19.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 16 days (c) 11 days (d) 15 days
20. 20.₹225 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹225 (b) ₹25 (c) ₹200 (d) ₹201
21. 21.If 7 pens cost ₹77, how much do 8 pens cost? (a) ₹616 (b) ₹88 (c) ₹78 (d) ₹99
22. 22.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 29 days (c) 13 days (d) 1 day
23. 23.₹343 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹147 (b) ₹49 (c) ₹245 (d) ₹196
24. 24.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 13 days (d) 1 day
25. 25.If 7 mangoes cost ₹105, how much do 8 mangoes cost? (a) ₹106 (b) ₹135 (c) ₹840 (d) ₹120
26. 26.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 13 days (b) 4 days (c) 2 days (d) 3 days
27. 27.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 10 days (c) 8 days (d) 9 days
28. 28.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 8 days (d) 1 day
29. 29.3 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 6 days (d) 24 days
30. 30.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 18 days (c) 5 days (d) 3 days
31. 31.₹28 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹7 (b) ₹14 (c) ₹28 (d) ₹21
32. 32.If 9 kites cost ₹135, how much do 8 kites cost? (a) ₹135 (b) ₹134 (c) ₹120 (d) ₹1080
33. 33.₹120 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹60 (b) ₹24 (c) ₹120 (d) ₹96
34. 34.₹342 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹152 (b) ₹171 (c) ₹38 (d) ₹190
35. 35.5 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) 17 days (d) 9 days
36. 36.If 4 notebooks cost ₹16, how much do 7 notebooks cost? (a) ₹19 (b) ₹32 (c) ₹28 (d) ₹112
37. 37.If 4 mangoes cost ₹76, how much do 2 mangoes cost? (a) ₹57 (b) ₹38 (c) ₹74 (d) ₹152
38. 38.₹70 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹7 (b) ₹21 (c) ₹35 (d) ₹49
39. 39.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 7 days (d) 3 days
40. 40.₹270 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹210 (b) ₹60 (c) ₹135 (d) ₹30

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