Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 951 · 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. 1.6 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 10 days (d) 14 days
2. 2.If 2 pens cost ₹8, how much do 6 pens cost? (a) ₹48 (b) ₹28 (c) ₹12 (d) ₹24
3. 3.If 7 kites cost ₹35, how much do 4 kites cost? (a) ₹32 (b) ₹140 (c) ₹25 (d) ₹20
4. 4.₹253 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹161 (b) ₹23 (c) ₹184 (d) ₹92
5. 5.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 4 days (c) 13 days (d) 7 days
6. 6.6 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 13 days (c) 9 days (d) 11 days
7. 7.If 3 notebooks cost ₹51, how much do 9 notebooks cost? (a) ₹459 (b) ₹57 (c) ₹153 (d) ₹170
8. 8.₹84 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹30 (b) ₹42 (c) ₹6 (d) ₹54
9. 9.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 11 days (d) 16 days
10. 10.If 4 pens cost ₹12, how much do 8 pens cost? (a) ₹16 (b) ₹24 (c) ₹27 (d) ₹96
11. 11.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 15 days (b) 20 days (c) 6 days (d) 5 days
12. 12.₹231 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹189 (b) ₹42 (c) ₹210 (d) ₹21
13. 13.If 2 notebooks cost ₹10, how much do 3 notebooks cost? (a) ₹15 (b) ₹20 (c) ₹30 (d) ₹11
14. 14.₹209 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹114 (b) ₹19 (c) ₹133 (d) ₹95
15. 15.If 5 pens cost ₹85, how much do 6 pens cost? (a) ₹102 (b) ₹86 (c) ₹510 (d) ₹119
16. 16.₹392 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹196 (b) ₹140 (c) ₹252 (d) ₹28
17. 17.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 11 days (d) 1 day
18. 18.₹200 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹20 (b) ₹100 (c) ₹200 (d) ₹180
19. 19.₹468 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹234 (b) ₹195 (c) ₹273 (d) ₹39
20. 20.If 2 mangoes cost ₹20, how much do 3 mangoes cost? (a) ₹21 (b) ₹40 (c) ₹60 (d) ₹30
21. 21.₹180 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹75 (b) ₹105 (c) ₹90 (d) ₹15
22. 22.If 7 mangoes cost ₹28, how much do 8 mangoes cost? (a) ₹32 (b) ₹36 (c) ₹29 (d) ₹224
23. 23.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 13 days (c) 27 days (d) 28 days
24. 24.8 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
25. 25.If 5 pens cost ₹25, how much do 4 pens cost? (a) ₹100 (b) ₹25 (c) ₹20 (d) ₹24
26. 26.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 19 days (c) 3 days (d) 4 days
27. 27.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 25 days (b) 16 days (c) 4 days (d) 5 days
28. 28.₹72 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹40 (b) ₹36 (c) ₹8 (d) ₹32
29. 29.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 14 days (c) 5 days (d) 15 days
30. 30.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 33 days (b) 17 days (c) 34 days (d) 5 days
31. 31.If 6 kites cost ₹36, how much do 11 kites cost? (a) ₹396 (b) ₹41 (c) ₹66 (d) ₹72
32. 32.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 17 days (d) 25 days
33. 33.If 5 notebooks cost ₹100, how much do 9 notebooks cost? (a) ₹200 (b) ₹900 (c) ₹104 (d) ₹180
34. 34.6 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 8 days (d) 10 days
35. 35.₹228 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹114 (b) ₹190 (c) ₹228 (d) ₹38
36. 36.₹416 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹288 (b) ₹32 (c) ₹208 (d) ₹128
37. 37.If 5 pens cost ₹25, how much do 8 pens cost? (a) ₹28 (b) ₹40 (c) ₹200 (d) ₹45
38. 38.If 2 kites cost ₹14, how much do 8 kites cost? (a) ₹20 (b) ₹56 (c) ₹112 (d) ₹63
39. 39.If 7 pens cost ₹140, how much do 12 pens cost? (a) ₹1680 (b) ₹145 (c) ₹260 (d) ₹240
40. 40.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 9 days (c) 1 day (d) 4 days

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