Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 165 · 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.₹377 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹261 (b) ₹232 (c) ₹145 (d) ₹29
2. 2.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 31 days (d) 30 days
3. 3.If 8 mangoes cost ₹56, how much do 3 mangoes cost? (a) ₹28 (b) ₹51 (c) ₹168 (d) ₹21
4. 4.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 5 days (d) 3 days
5. 5.If 9 kites cost ₹36, how much do 2 kites cost? (a) ₹72 (b) ₹29 (c) ₹12 (d) ₹8
6. 6.6 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 20 days (b) 13 days (c) 5 days (d) 7 days
7. 7.If 5 kites cost ₹110, how much do 9 kites cost? (a) ₹990 (b) ₹114 (c) ₹198 (d) ₹220
8. 8.₹48 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹24 (b) ₹30 (c) ₹6 (d) ₹18
9. 9.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 12 days (c) 13 days (d) 10 days
10. 10.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 25 days (b) 13 days (c) 17 days (d) 9 days
11. 11.If 9 pens cost ₹99, how much do 7 pens cost? (a) ₹88 (b) ₹693 (c) ₹97 (d) ₹77
12. 12.If 3 notebooks cost ₹27, how much do 4 notebooks cost? (a) ₹108 (b) ₹36 (c) ₹28 (d) ₹45
13. 13.If 5 kites cost ₹95, how much do 6 kites cost? (a) ₹96 (b) ₹114 (c) ₹133 (d) ₹570
14. 14.₹210 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹15 (b) ₹75 (c) ₹135 (d) ₹105
15. 15.₹259 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹222 (b) ₹37 (c) ₹185 (d) ₹74
16. 16.If 7 notebooks cost ₹84, how much do 3 notebooks cost? (a) ₹36 (b) ₹252 (c) ₹80 (d) ₹48
17. 17.If 7 kites cost ₹126, how much do 5 kites cost? (a) ₹108 (b) ₹124 (c) ₹90 (d) ₹630
18. 18.₹576 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹288 (b) ₹240 (c) ₹48 (d) ₹336
19. 19.If 4 kites cost ₹44, how much do 12 kites cost? (a) ₹52 (b) ₹132 (c) ₹143 (d) ₹528
20. 20.₹45 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹40 (b) ₹5 (c) ₹35 (d) ₹10
21. 21.3 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) 7 days (d) 2 days
22. 22.₹264 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹96 (b) ₹24 (c) ₹168 (d) ₹132
23. 23.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 22 days (c) 13 days (d) 21 days
24. 24.If 9 mangoes cost ₹171, how much do 7 mangoes cost? (a) ₹169 (b) ₹133 (c) ₹152 (d) ₹1197
25. 25.If 5 notebooks cost ₹15, how much do 7 notebooks cost? (a) ₹105 (b) ₹21 (c) ₹17 (d) ₹24
26. 26.₹110 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹10 (b) ₹55 (c) ₹30 (d) ₹80
27. 27.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 19 days
28. 28.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 10 days (c) 4 days (d) 3 days
29. 29.If 7 notebooks cost ₹133, how much do 8 notebooks cost? (a) ₹134 (b) ₹1064 (c) ₹152 (d) ₹171
30. 30.₹180 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹20 (b) ₹100 (c) ₹80 (d) ₹90
31. 31.If 5 kites cost ₹50, how much do 8 kites cost? (a) ₹53 (b) ₹400 (c) ₹90 (d) ₹80
32. 32.If 5 pens cost ₹105, how much do 6 pens cost? (a) ₹126 (b) ₹630 (c) ₹147 (d) ₹106
33. 33.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 9 days (d) 10 days
34. 34.If 6 mangoes cost ₹132, how much do 9 mangoes cost? (a) ₹198 (b) ₹1188 (c) ₹220 (d) ₹135
35. 35.If 3 notebooks cost ₹75, how much do 7 notebooks cost? (a) ₹525 (b) ₹175 (c) ₹200 (d) ₹79
36. 36.If 3 pens cost ₹12, how much do 8 pens cost? (a) ₹17 (b) ₹96 (c) ₹32 (d) ₹36
37. 37.₹208 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹104 (b) ₹64 (c) ₹16 (d) ₹144
38. 38.₹319 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹203 (b) ₹29 (c) ₹174 (d) ₹145
39. 39.If 2 mangoes cost ₹14, how much do 3 mangoes cost? (a) ₹42 (b) ₹15 (c) ₹28 (d) ₹21
40. 40.₹266 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹133 (b) ₹114 (c) ₹152 (d) ₹38

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