Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 778 · 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.₹70 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹28 (b) ₹35 (c) ₹42 (d) ₹14
2. 2.If 2 notebooks cost ₹30, how much do 3 notebooks cost? (a) ₹31 (b) ₹45 (c) ₹90 (d) ₹60
3. 3.₹54 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹45 (b) ₹54 (c) ₹9 (d) ₹27
4. 4.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 5 days (d) 14 days
5. 5.₹240 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹192 (b) ₹120 (c) ₹240 (d) ₹48
6. 6.₹169 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹13 (b) ₹52 (c) ₹117 (d) ₹130
7. 7.₹616 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹396 (b) ₹220 (c) ₹44 (d) ₹308
8. 8.₹517 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹329 (b) ₹47 (c) ₹235 (d) ₹282
9. 9.₹407 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹296 (b) ₹148 (c) ₹37 (d) ₹259
10. 10.₹88 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹77 (b) ₹44 (c) ₹11 (d) ₹88
11. 11.₹192 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹32 (b) ₹160 (c) ₹192 (d) ₹96
12. 12.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 3 days (d) 28 days
13. 13.₹455 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹35 (b) ₹140 (c) ₹315 (d) ₹350
14. 14.If 4 notebooks cost ₹44, how much do 5 notebooks cost? (a) ₹66 (b) ₹220 (c) ₹45 (d) ₹55
15. 15.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 11 days (d) 26 days
16. 16.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 36 days (c) 15 days (d) 37 days
17. 17.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 15 days (c) 9 days (d) 14 days
18. 18.₹336 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹96 (b) ₹240 (c) ₹168 (d) ₹48
19. 19.3 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 6 days (b) 15 days (c) 9 days (d) 24 days
20. 20.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 6 days (c) 10 days (d) 4 days
21. 21.₹63 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹56 (b) ₹63 (c) ₹7 (d) ₹57
22. 22.If 5 pens cost ₹45, how much do 12 pens cost? (a) ₹52 (b) ₹108 (c) ₹117 (d) ₹540
23. 23.₹190 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹19 (b) ₹95 (c) ₹133 (d) ₹57
24. 24.If 9 mangoes cost ₹99, how much do 6 mangoes cost? (a) ₹77 (b) ₹66 (c) ₹96 (d) ₹594
25. 25.If 6 notebooks cost ₹54, how much do 5 notebooks cost? (a) ₹270 (b) ₹45 (c) ₹53 (d) ₹54
26. 26.If 7 kites cost ₹175, how much do 2 kites cost? (a) ₹75 (b) ₹170 (c) ₹350 (d) ₹50
27. 27.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 34 days (b) 7 days (c) 33 days (d) 15 days
28. 28.₹126 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹63 (b) ₹90 (c) ₹18 (d) ₹36
29. 29.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 32 days (b) 14 days (c) 2 days (d) 33 days
30. 30.If 5 kites cost ₹20, how much do 10 kites cost? (a) ₹40 (b) ₹25 (c) ₹200 (d) ₹44
31. 31.If 2 pens cost ₹8, how much do 11 pens cost? (a) ₹17 (b) ₹48 (c) ₹44 (d) ₹88
32. 32.If 7 pens cost ₹112, how much do 10 pens cost? (a) ₹115 (b) ₹176 (c) ₹1120 (d) ₹160
33. 33.₹120 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹60 (b) ₹20 (c) ₹120 (d) ₹100
34. 34.If 9 mangoes cost ₹180, how much do 10 mangoes cost? (a) ₹181 (b) ₹1800 (c) ₹220 (d) ₹200
35. 35.6 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 6 days (d) 10 days
36. 36.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 11 days (d) 3 days
37. 37.If 4 mangoes cost ₹76, how much do 12 mangoes cost? (a) ₹228 (b) ₹912 (c) ₹84 (d) ₹247
38. 38.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 19 days (c) 39 days (d) 40 days
39. 39.₹56 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹16 (b) ₹28 (c) ₹40 (d) ₹8
40. 40.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 15 days (c) 3 days (d) 27 days

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