Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 486 · 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. 1.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 13 days (d) 14 days
2. 2.If 4 kites cost ₹96, how much do 11 kites cost? (a) ₹1056 (b) ₹288 (c) ₹264 (d) ₹103
3. 3.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 8 days (c) 18 days (d) 11 days
4. 4.If 9 pens cost ₹54, how much do 12 pens cost? (a) ₹57 (b) ₹72 (c) ₹648 (d) ₹78
5. 5.If 8 kites cost ₹120, how much do 3 kites cost? (a) ₹360 (b) ₹60 (c) ₹45 (d) ₹115
6. 6.₹54 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹27 (b) ₹30 (c) ₹6 (d) ₹24
7. 7.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 1 day (c) 9 days (d) 11 days
8. 8.If 9 kites cost ₹180, how much do 2 kites cost? (a) ₹60 (b) ₹40 (c) ₹173 (d) ₹360
9. 9.If 5 notebooks cost ₹75, how much do 9 notebooks cost? (a) ₹675 (b) ₹150 (c) ₹79 (d) ₹135
10. 10.₹440 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹160 (b) ₹220 (c) ₹40 (d) ₹280
11. 11.If 5 kites cost ₹55, how much do 10 kites cost? (a) ₹60 (b) ₹121 (c) ₹110 (d) ₹550
12. 12.If 3 kites cost ₹42, how much do 10 kites cost? (a) ₹140 (b) ₹420 (c) ₹49 (d) ₹154
13. 13.₹238 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹153 (b) ₹17 (c) ₹119 (d) ₹85
14. 14.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 1 day (d) 9 days
15. 15.₹336 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹96 (b) ₹48 (c) ₹168 (d) ₹240
16. 16.If 3 notebooks cost ₹51, how much do 6 notebooks cost? (a) ₹306 (b) ₹102 (c) ₹54 (d) ₹119
17. 17.If 4 pens cost ₹32, how much do 5 pens cost? (a) ₹40 (b) ₹160 (c) ₹48 (d) ₹33
18. 18.₹390 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹30 (b) ₹150 (c) ₹195 (d) ₹240
19. 19.₹333 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹296 (b) ₹297 (c) ₹333 (d) ₹37
20. 20.₹372 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹31 (b) ₹217 (c) ₹155 (d) ₹186
21. 21.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 15 days (b) 17 days (c) 16 days (d) 13 days
22. 22.If 4 pens cost ₹16, how much do 3 pens cost? (a) ₹48 (b) ₹15 (c) ₹16 (d) ₹12
23. 23.₹320 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹160 (b) ₹32 (c) ₹96 (d) ₹224
24. 24.₹324 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹144 (b) ₹36 (c) ₹180 (d) ₹162
25. 25.If 9 pens cost ₹54, how much do 10 pens cost? (a) ₹66 (b) ₹55 (c) ₹60 (d) ₹540
26. 26.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 2 days (b) 12 days (c) 3 days (d) 18 days
27. 27.₹336 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹168 (b) ₹48 (c) ₹192 (d) ₹144
28. 28.If 8 notebooks cost ₹32, how much do 9 notebooks cost? (a) ₹33 (b) ₹40 (c) ₹288 (d) ₹36
29. 29.₹198 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹99 (b) ₹108 (c) ₹90 (d) ₹18
30. 30.₹70 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹45 (b) ₹35 (c) ₹5 (d) ₹25
31. 31.₹374 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹187 (b) ₹238 (c) ₹136 (d) ₹34
32. 32.If 9 pens cost ₹45, how much do 5 pens cost? (a) ₹225 (b) ₹41 (c) ₹30 (d) ₹25
33. 33.If 4 mangoes cost ₹44, how much do 10 mangoes cost? (a) ₹50 (b) ₹440 (c) ₹121 (d) ₹110
34. 34.If 3 mangoes cost ₹45, how much do 7 mangoes cost? (a) ₹105 (b) ₹315 (c) ₹120 (d) ₹49
35. 35.If 9 notebooks cost ₹126, how much do 6 notebooks cost? (a) ₹84 (b) ₹756 (c) ₹123 (d) ₹98
36. 36.If 8 notebooks cost ₹200, how much do 5 notebooks cost? (a) ₹150 (b) ₹1000 (c) ₹125 (d) ₹197
37. 37.₹360 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹40 (b) ₹320 (c) ₹180 (d) ₹360
38. 38.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 9 days (d) 25 days
39. 39.If 3 kites cost ₹72, how much do 11 kites cost? (a) ₹288 (b) ₹80 (c) ₹264 (d) ₹792
40. 40.If 7 pens cost ₹84, how much do 2 pens cost? (a) ₹168 (b) ₹79 (c) ₹36 (d) ₹24

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