Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 652 · 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. 1.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 9 days (d) 8 days
2. 2.₹484 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹176 (b) ₹242 (c) ₹308 (d) ₹44
3. 3.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 5 days (c) 36 days (d) 35 days
4. 4.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 12 days (d) 5 days
5. 5.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 11 days (d) 13 days
6. 6.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 4 days (d) 3 days
7. 7.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 36 days (d) 18 days
8. 8.If 8 pens cost ₹120, how much do 7 pens cost? (a) ₹840 (b) ₹105 (c) ₹120 (d) ₹119
9. 9.₹30 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹30 (b) ₹6 (c) ₹15 (d) ₹24
10. 10.9 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 11 days (c) 10 days (d) 9 days
11. 11.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 7 days (d) 8 days
12. 12.If 6 pens cost ₹36, how much do 12 pens cost? (a) ₹78 (b) ₹42 (c) ₹72 (d) ₹432
13. 13.₹220 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹66 (b) ₹154 (c) ₹110 (d) ₹22
14. 14.₹175 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹75 (b) ₹25 (c) ₹125 (d) ₹100
15. 15.If 7 pens cost ₹98, how much do 6 pens cost? (a) ₹588 (b) ₹97 (c) ₹84 (d) ₹98
16. 16.₹270 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹135 (b) ₹60 (c) ₹30 (d) ₹210
17. 17.₹341 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹217 (b) ₹124 (c) ₹31 (d) ₹248
18. 18.If 8 notebooks cost ₹176, how much do 6 notebooks cost? (a) ₹1056 (b) ₹132 (c) ₹174 (d) ₹154
19. 19.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 21 days (d) 45 days
20. 20.If 7 kites cost ₹63, how much do 6 kites cost? (a) ₹378 (b) ₹54 (c) ₹62 (d) ₹63
21. 21.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 12 days (c) 10 days (d) 2 days
22. 22.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 2 days (d) 7 days
23. 23.If 8 pens cost ₹40, how much do 6 pens cost? (a) ₹38 (b) ₹240 (c) ₹35 (d) ₹30
24. 24.₹30 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹15 (b) ₹25 (c) ₹5 (d) ₹30
25. 25.₹598 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹230 (b) ₹299 (c) ₹368 (d) ₹46
26. 26.₹637 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹490 (b) ₹196 (c) ₹441 (d) ₹49
27. 27.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 4 days (d) 14 days
28. 28.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 7 days (d) 3 days
29. 29.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 11 days (d) 13 days
30. 30.₹252 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹147 (b) ₹105 (c) ₹126 (d) ₹21
31. 31.₹192 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹192 (b) ₹168 (c) ₹24 (d) ₹96
32. 32.₹481 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹370 (b) ₹37 (c) ₹333 (d) ₹148
33. 33.If 9 pens cost ₹27, how much do 11 pens cost? (a) ₹29 (b) ₹297 (c) ₹33 (d) ₹36
34. 34.If 5 notebooks cost ₹50, how much do 9 notebooks cost? (a) ₹100 (b) ₹90 (c) ₹54 (d) ₹450
35. 35.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 17 days (d) 4 days
36. 36.If 2 kites cost ₹32, how much do 9 kites cost? (a) ₹144 (b) ₹160 (c) ₹39 (d) ₹288
37. 37.3 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 24 days (d) 6 days
38. 38.If 4 notebooks cost ₹64, how much do 10 notebooks cost? (a) ₹640 (b) ₹160 (c) ₹70 (d) ₹176
39. 39.₹440 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹160 (b) ₹40 (c) ₹280 (d) ₹220
40. 40.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 22 days (c) 21 days (d) 3 days

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