Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 158 · 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 6 days. How many days will 6 workers take, working at the same speed? (a) 12 days (b) 3 days (c) 9 days (d) 4 days
2. 2.If 7 mangoes cost ₹133, how much do 8 mangoes cost? (a) ₹134 (b) ₹1064 (c) ₹171 (d) ₹152
3. 3.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 12 days (c) 2 days (d) 18 days
4. 4.If 8 kites cost ₹80, how much do 9 kites cost? (a) ₹90 (b) ₹720 (c) ₹81 (d) ₹100
5. 5.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 6 days (c) 4 days (d) 5 days
6. 6.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 2 days (d) 9 days
7. 7.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 8 days (d) 9 days
8. 8.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 3 days (c) 2 days (d) 8 days
9. 9.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 6 days (c) 19 days (d) 12 days
10. 10.If 5 kites cost ₹85, how much do 6 kites cost? (a) ₹102 (b) ₹119 (c) ₹510 (d) ₹86
11. 11.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 27 days (d) 4 days
12. 12.If 5 notebooks cost ₹20, how much do 3 notebooks cost? (a) ₹16 (b) ₹18 (c) ₹12 (d) ₹60
13. 13.8 workers can build a wall in 9 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 19 days (c) 13 days (d) 18 days
14. 14.If 3 mangoes cost ₹66, how much do 9 mangoes cost? (a) ₹72 (b) ₹220 (c) ₹198 (d) ₹594
15. 15.If 6 kites cost ₹24, how much do 11 kites cost? (a) ₹44 (b) ₹48 (c) ₹264 (d) ₹29
16. 16.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 43 days (c) 42 days (d) 7 days
17. 17.₹546 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹273 (b) ₹351 (c) ₹39 (d) ₹195
18. 18.If 6 pens cost ₹78, how much do 12 pens cost? (a) ₹936 (b) ₹84 (c) ₹169 (d) ₹156
19. 19.₹462 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹231 (b) ₹252 (c) ₹42 (d) ₹210
20. 20.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 21 days (d) 22 days
21. 21.If 9 mangoes cost ₹99, how much do 4 mangoes cost? (a) ₹44 (b) ₹94 (c) ₹55 (d) ₹396
22. 22.If 9 kites cost ₹36, how much do 2 kites cost? (a) ₹72 (b) ₹8 (c) ₹29 (d) ₹12
23. 23.If 6 notebooks cost ₹102, how much do 7 notebooks cost? (a) ₹714 (b) ₹119 (c) ₹136 (d) ₹103
24. 24.If 3 notebooks cost ₹60, how much do 4 notebooks cost? (a) ₹240 (b) ₹80 (c) ₹61 (d) ₹100
25. 25.₹60 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹30 (b) ₹6 (c) ₹42 (d) ₹18
26. 26.₹78 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹30 (b) ₹48 (c) ₹39 (d) ₹6
27. 27.₹279 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹186 (b) ₹155 (c) ₹31 (d) ₹124
28. 28.If 9 kites cost ₹153, how much do 7 kites cost? (a) ₹136 (b) ₹119 (c) ₹1071 (d) ₹151
29. 29.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 7 days
30. 30.If 4 mangoes cost ₹60, how much do 5 mangoes cost? (a) ₹90 (b) ₹300 (c) ₹61 (d) ₹75
31. 31.₹294 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹147 (b) ₹84 (c) ₹210 (d) ₹42
32. 32.₹110 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹55 (b) ₹22 (c) ₹66 (d) ₹44
33. 33.If 6 pens cost ₹108, how much do 12 pens cost? (a) ₹114 (b) ₹234 (c) ₹216 (d) ₹1296
34. 34.If 2 pens cost ₹46, how much do 4 pens cost? (a) ₹48 (b) ₹184 (c) ₹92 (d) ₹115
35. 35.If 5 pens cost ₹115, how much do 4 pens cost? (a) ₹115 (b) ₹92 (c) ₹114 (d) ₹460
36. 36.₹150 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹75 (b) ₹90 (c) ₹60 (d) ₹30
37. 37.₹147 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹127 (b) ₹21 (c) ₹126 (d) ₹147
38. 38.₹363 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹231 (b) ₹33 (c) ₹264 (d) ₹132
39. 39.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 3 days (d) 7 days
40. 40.If 7 pens cost ₹154, how much do 10 pens cost? (a) ₹157 (b) ₹242 (c) ₹1540 (d) ₹220

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