Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 651 · 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. 1.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 19 days (d) 2 days
2. 2.If 8 pens cost ₹56, how much do 9 pens cost? (a) ₹63 (b) ₹57 (c) ₹504 (d) ₹70
3. 3.9 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 9 days (d) 8 days
4. 4.If 6 kites cost ₹24, how much do 10 kites cost? (a) ₹40 (b) ₹28 (c) ₹44 (d) ₹240
5. 5.If 7 notebooks cost ₹35, how much do 2 notebooks cost? (a) ₹70 (b) ₹30 (c) ₹15 (d) ₹10
6. 6.If 7 mangoes cost ₹126, how much do 8 mangoes cost? (a) ₹127 (b) ₹144 (c) ₹1008 (d) ₹162
7. 7.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 21 days (d) 6 days
8. 8.If 8 mangoes cost ₹56, how much do 4 mangoes cost? (a) ₹28 (b) ₹52 (c) ₹35 (d) ₹224
9. 9.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 14 days (c) 11 days (d) 15 days
10. 10.If 3 kites cost ₹36, how much do 2 kites cost? (a) ₹35 (b) ₹24 (c) ₹36 (d) ₹72
11. 11.If 4 mangoes cost ₹32, how much do 2 mangoes cost? (a) ₹16 (b) ₹24 (c) ₹30 (d) ₹64
12. 12.If 7 notebooks cost ₹21, how much do 8 notebooks cost? (a) ₹27 (b) ₹22 (c) ₹24 (d) ₹168
13. 13.If 7 mangoes cost ₹105, how much do 10 mangoes cost? (a) ₹108 (b) ₹150 (c) ₹1050 (d) ₹165
14. 14.If 3 pens cost ₹9, how much do 4 pens cost? (a) ₹12 (b) ₹15 (c) ₹36 (d) ₹10
15. 15.₹222 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹222 (b) ₹111 (c) ₹185 (d) ₹37
16. 16.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 3 days (d) 1 day
17. 17.8 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 7 days (d) 9 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. 19.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 6 days (d) 4 days
20. 20.If 8 pens cost ₹48, how much do 9 pens cost? (a) ₹54 (b) ₹432 (c) ₹49 (d) ₹60
21. 21.₹275 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹25 (b) ₹150 (c) ₹175 (d) ₹125
22. 22.If 6 pens cost ₹30, how much do 10 pens cost? (a) ₹34 (b) ₹55 (c) ₹300 (d) ₹50
23. 23.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 43 days (c) 42 days (d) 18 days
24. 24.₹198 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹176 (b) ₹99 (c) ₹198 (d) ₹22
25. 25.₹416 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹208 (b) ₹288 (c) ₹128 (d) ₹32
26. 26.₹175 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹140 (b) ₹35 (c) ₹105 (d) ₹70
27. 27.If 9 kites cost ₹162, how much do 4 kites cost? (a) ₹72 (b) ₹157 (c) ₹90 (d) ₹648
28. 28.9 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 24 days (b) 2 days (c) 25 days (d) 14 days
29. 29.5 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 21 days (c) 20 days (d) 10 days
30. 30.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 4 days (d) 9 days
31. 31.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 1 day (c) 11 days (d) 17 days
32. 32.₹588 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹49 (b) ₹343 (c) ₹294 (d) ₹245
33. 33.₹280 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹280 (b) ₹140 (c) ₹252 (d) ₹28
34. 34.If 4 notebooks cost ₹24, how much do 9 notebooks cost? (a) ₹216 (b) ₹60 (c) ₹29 (d) ₹54
35. 35.₹90 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹10 (b) ₹45 (c) ₹70 (d) ₹20
36. 36.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 34 days (c) 33 days (d) 15 days
37. 37.If 7 notebooks cost ₹42, how much do 9 notebooks cost? (a) ₹54 (b) ₹44 (c) ₹378 (d) ₹60
38. 38.₹110 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹55 (b) ₹10 (c) ₹60 (d) ₹50
39. 39.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹84 (b) ₹12 (c) ₹108 (d) ₹60
40. 40.₹80 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹40 (b) ₹16 (c) ₹80 (d) ₹64

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