Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 725 · 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 12 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 36 days (c) 4 days (d) 6 days
2. 2.If 8 pens cost ₹168, how much do 12 pens cost? (a) ₹172 (b) ₹273 (c) ₹252 (d) ₹2016
3. 3.₹84 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹48 (b) ₹12 (c) ₹42 (d) ₹36
4. 4.₹506 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹253 (b) ₹46 (c) ₹276 (d) ₹230
5. 5.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 17 days (b) 15 days (c) 13 days (d) 16 days
6. 6.If 8 mangoes cost ₹200, how much do 6 mangoes cost? (a) ₹175 (b) ₹198 (c) ₹1200 (d) ₹150
7. 7.9 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 6 days (d) 11 days
8. 8.8 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 24 days (d) 16 days
9. 9.If 5 notebooks cost ₹25, how much do 7 notebooks cost? (a) ₹27 (b) ₹35 (c) ₹175 (d) ₹40
10. 10.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 13 days (c) 3 days (d) 5 days
11. 11.9 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 14 days (c) 18 days (d) 19 days
12. 12.If 5 pens cost ₹60, how much do 2 pens cost? (a) ₹120 (b) ₹24 (c) ₹36 (d) ₹57
13. 13.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 12 days (c) 24 days (d) 23 days
14. 14.₹407 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹333 (b) ₹370 (c) ₹74 (d) ₹37
15. 15.₹140 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹105 (b) ₹70 (c) ₹140 (d) ₹35
16. 16.If 4 notebooks cost ₹40, how much do 8 notebooks cost? (a) ₹320 (b) ₹44 (c) ₹80 (d) ₹90
17. 17.If 6 mangoes cost ₹60, how much do 5 mangoes cost? (a) ₹50 (b) ₹300 (c) ₹59 (d) ₹60
18. 18.If 4 notebooks cost ₹84, how much do 3 notebooks cost? (a) ₹252 (b) ₹63 (c) ₹83 (d) ₹84
19. 19.₹112 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹56 (b) ₹112 (c) ₹84 (d) ₹28
20. 20.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 21 days (d) 22 days
21. 21.If 2 notebooks cost ₹20, how much do 3 notebooks cost? (a) ₹30 (b) ₹40 (c) ₹60 (d) ₹21
22. 22.If 2 pens cost ₹40, how much do 12 pens cost? (a) ₹50 (b) ₹240 (c) ₹480 (d) ₹260
23. 23.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 18 days (c) 7 days (d) 11 days
24. 24.₹144 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹144 (b) ₹128 (c) ₹72 (d) ₹16
25. 25.₹104 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹26 (b) ₹104 (c) ₹78 (d) ₹52
26. 26.₹407 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹148 (b) ₹37 (c) ₹296 (d) ₹259
27. 27.₹350 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹175 (b) ₹25 (c) ₹125 (d) ₹225
28. 28.If 2 notebooks cost ₹46, how much do 9 notebooks cost? (a) ₹207 (b) ₹53 (c) ₹230 (d) ₹414
29. 29.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 25 days (d) 13 days
30. 30.If 3 kites cost ₹45, how much do 10 kites cost? (a) ₹52 (b) ₹150 (c) ₹165 (d) ₹450
31. 31.₹325 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹25 (b) ₹200 (c) ₹225 (d) ₹125
32. 32.₹180 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹90 (b) ₹36 (c) ₹72 (d) ₹108
33. 33.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 6 days (d) 4 days
34. 34.If 9 kites cost ₹72, how much do 6 kites cost? (a) ₹432 (b) ₹69 (c) ₹56 (d) ₹48
35. 35.₹320 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹224 (b) ₹160 (c) ₹96 (d) ₹32
36. 36.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 11 days (c) 27 days (d) 15 days
37. 37.If 3 kites cost ₹57, how much do 11 kites cost? (a) ₹65 (b) ₹209 (c) ₹627 (d) ₹228
38. 38.If 7 notebooks cost ₹56, how much do 4 notebooks cost? (a) ₹224 (b) ₹40 (c) ₹53 (d) ₹32
39. 39.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹35 (b) ₹7 (c) ₹56 (d) ₹63
40. 40.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 11 days (c) 22 days (d) 21 days

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