Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 829 · 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. 1.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 15 days (d) 16 days
2. 2.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 4 days (d) 2 days
3. 3.₹300 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹150 (b) ₹270 (c) ₹300 (d) ₹30
4. 4.₹66 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹30 (b) ₹33 (c) ₹6 (d) ₹36
5. 5.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 27 days (b) 26 days (c) 17 days (d) 9 days
6. 6.If 9 pens cost ₹198, how much do 10 pens cost? (a) ₹242 (b) ₹1980 (c) ₹199 (d) ₹220
7. 7.₹70 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹35 (b) ₹25 (c) ₹45 (d) ₹5
8. 8.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 2 days (d) 10 days
9. 9.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 4 days (d) 5 days
10. 10.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 13 days (c) 7 days (d) 4 days
11. 11.If 6 mangoes cost ₹126, how much do 11 mangoes cost? (a) ₹231 (b) ₹1386 (c) ₹252 (d) ₹131
12. 12.If 7 kites cost ₹98, how much do 10 kites cost? (a) ₹980 (b) ₹154 (c) ₹101 (d) ₹140
13. 13.9 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 30 days (c) 16 days (d) 31 days
14. 14.₹18 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹18 (b) ₹12 (c) ₹6 (d) ₹9
15. 15.6 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
16. 16.₹217 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹186 (b) ₹31 (c) ₹155 (d) ₹62
17. 17.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 13 days (c) 26 days (d) 28 days
18. 18.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 12 days (d) 13 days
19. 19.If 6 kites cost ₹42, how much do 2 kites cost? (a) ₹21 (b) ₹38 (c) ₹84 (d) ₹14
20. 20.₹98 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹7 (b) ₹63 (c) ₹35 (d) ₹49
21. 21.₹243 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹217 (b) ₹243 (c) ₹216 (d) ₹27
22. 22.₹121 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹44 (b) ₹11 (c) ₹88 (d) ₹77
23. 23.9 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 18 days (c) 19 days (d) 13 days
24. 24.4 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 18 days (c) 14 days (d) 10 days
25. 25.If 8 kites cost ₹168, how much do 6 kites cost? (a) ₹126 (b) ₹1008 (c) ₹166 (d) ₹147
26. 26.₹247 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹19 (b) ₹152 (c) ₹95 (d) ₹171
27. 27.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 25 days (d) 13 days
28. 28.₹616 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹220 (b) ₹44 (c) ₹308 (d) ₹396
29. 29.6 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 16 days (b) 6 days (c) 5 days (d) 7 days
30. 30.If 8 pens cost ₹48, how much do 7 pens cost? (a) ₹336 (b) ₹48 (c) ₹47 (d) ₹42
31. 31.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 57 days (b) 56 days (c) 20 days (d) 8 days
32. 32.If 2 pens cost ₹46, how much do 4 pens cost? (a) ₹92 (b) ₹115 (c) ₹184 (d) ₹48
33. 33.If 8 notebooks cost ₹24, how much do 12 notebooks cost? (a) ₹36 (b) ₹39 (c) ₹28 (d) ₹288
34. 34.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 4 days (d) 5 days
35. 35.If 2 pens cost ₹46, how much do 8 pens cost? (a) ₹52 (b) ₹368 (c) ₹184 (d) ₹207
36. 36.If 7 mangoes cost ₹91, how much do 8 mangoes cost? (a) ₹728 (b) ₹104 (c) ₹92 (d) ₹117
37. 37.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 43 days (b) 7 days (c) 42 days (d) 17 days
38. 38.If 2 mangoes cost ₹12, how much do 5 mangoes cost? (a) ₹15 (b) ₹60 (c) ₹36 (d) ₹30
39. 39.If 8 pens cost ₹136, how much do 9 pens cost? (a) ₹153 (b) ₹137 (c) ₹1224 (d) ₹170
40. 40.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 2 days (c) 15 days (d) 10 days

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