Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 17 · 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 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 3 days (d) 2 days
2. 2.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 22 days (c) 14 days (d) 23 days
3. 3.₹248 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹124 (b) ₹248 (c) ₹31 (d) ₹217
4. 4.₹125 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹101 (b) ₹125 (c) ₹100 (d) ₹25
5. 5.₹374 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹34 (b) ₹187 (c) ₹204 (d) ₹170
6. 6.5 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
7. 7.₹50 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹5 (b) ₹25 (c) ₹45 (d) ₹50
8. 8.₹160 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹48 (b) ₹80 (c) ₹112 (d) ₹16
9. 9.₹190 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹95 (b) ₹19 (c) ₹57 (d) ₹133
10. 10.If 6 notebooks cost ₹42, how much do 2 notebooks cost? (a) ₹14 (b) ₹21 (c) ₹38 (d) ₹84
11. 11.If 2 mangoes cost ₹42, how much do 4 mangoes cost? (a) ₹168 (b) ₹84 (c) ₹105 (d) ₹44
12. 12.₹360 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹40 (b) ₹160 (c) ₹200 (d) ₹180
13. 13.If 3 notebooks cost ₹36, how much do 8 notebooks cost? (a) ₹288 (b) ₹96 (c) ₹41 (d) ₹108
14. 14.₹105 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹84 (b) ₹105 (c) ₹21 (d) ₹85
15. 15.₹70 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹28 (b) ₹14 (c) ₹42 (d) ₹35
16. 16.4 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 14 days (b) 12 days (c) 16 days (d) 13 days
17. 17.₹280 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹35 (b) ₹245 (c) ₹140 (d) ₹280
18. 18.If 2 pens cost ₹14, how much do 6 pens cost? (a) ₹18 (b) ₹42 (c) ₹49 (d) ₹84
19. 19.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 2 days (d) 8 days
20. 20.If 5 notebooks cost ₹100, how much do 4 notebooks cost? (a) ₹99 (b) ₹100 (c) ₹80 (d) ₹400
21. 21.If 8 kites cost ₹24, how much do 12 kites cost? (a) ₹39 (b) ₹288 (c) ₹36 (d) ₹28
22. 22.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 28 days (c) 7 days (d) 16 days
23. 23.₹77 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹33 (b) ₹55 (c) ₹44 (d) ₹11
24. 24.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 2 days (c) 15 days (d) 14 days
25. 25.If 7 mangoes cost ₹140, how much do 9 mangoes cost? (a) ₹142 (b) ₹200 (c) ₹1260 (d) ₹180
26. 26.₹152 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹19 (b) ₹76 (c) ₹57 (d) ₹95
27. 27.6 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 16 days (b) 5 days (c) 7 days (d) 6 days
28. 28.₹165 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹15 (b) ₹75 (c) ₹90 (d) ₹105
29. 29.If 4 pens cost ₹72, how much do 5 pens cost? (a) ₹360 (b) ₹108 (c) ₹90 (d) ₹73
30. 30.₹480 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹48 (b) ₹336 (c) ₹144 (d) ₹240
31. 31.If 9 mangoes cost ₹72, how much do 6 mangoes cost? (a) ₹432 (b) ₹69 (c) ₹48 (d) ₹56
32. 32.If 7 pens cost ₹175, how much do 3 pens cost? (a) ₹100 (b) ₹525 (c) ₹75 (d) ₹171
33. 33.If 7 kites cost ₹133, how much do 10 kites cost? (a) ₹1330 (b) ₹136 (c) ₹190 (d) ₹209
34. 34.8 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) 16 days (d) 15 days
35. 35.If 7 kites cost ₹98, how much do 3 kites cost? (a) ₹56 (b) ₹42 (c) ₹294 (d) ₹94
36. 36.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 18 days (c) 11 days (d) 10 days
37. 37.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 22 days (c) 11 days (d) 21 days
38. 38.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 27 days (d) 26 days
39. 39.If 4 mangoes cost ₹100, how much do 7 mangoes cost? (a) ₹175 (b) ₹700 (c) ₹200 (d) ₹103
40. 40.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 10 days (c) 3 days (d) 5 days

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