Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 462 · 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.₹45 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹40 (b) ₹5 (c) ₹45 (d) ₹41
2. 2.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 10 days (d) 3 days
3. 3.9 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 28 days (c) 27 days (d) 17 days
4. 4.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 14 days (c) 15 days (d) 10 days
5. 5.₹576 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹288 (b) ₹336 (c) ₹48 (d) ₹240
6. 6.₹473 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹43 (b) ₹301 (c) ₹258 (d) ₹215
7. 7.If 2 kites cost ₹22, how much do 10 kites cost? (a) ₹121 (b) ₹220 (c) ₹110 (d) ₹30
8. 8.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 11 days (d) 6 days
9. 9.If 6 pens cost ₹138, how much do 8 pens cost? (a) ₹184 (b) ₹140 (c) ₹1104 (d) ₹207
10. 10.₹176 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹16 (b) ₹88 (c) ₹144 (d) ₹32
11. 11.₹112 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹64 (b) ₹56 (c) ₹16 (d) ₹48
12. 12.₹117 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹72 (b) ₹81 (c) ₹45 (d) ₹9
13. 13.If 4 notebooks cost ₹48, how much do 3 notebooks cost? (a) ₹47 (b) ₹144 (c) ₹48 (d) ₹36
14. 14.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 3 days (d) 7 days
15. 15.₹66 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹55 (b) ₹66 (c) ₹11 (d) ₹33
16. 16.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 7 days (d) 6 days
17. 17.If 8 mangoes cost ₹200, how much do 12 mangoes cost? (a) ₹2400 (b) ₹325 (c) ₹300 (d) ₹204
18. 18.6 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 14 days (c) 5 days (d) 6 days
19. 19.₹517 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹329 (b) ₹376 (c) ₹47 (d) ₹188
20. 20.₹156 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹12 (b) ₹78 (c) ₹108 (d) ₹48
21. 21.₹99 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹67 (b) ₹33 (c) ₹66 (d) ₹99
22. 22.₹143 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹117 (b) ₹39 (c) ₹13 (d) ₹104
23. 23.If 4 pens cost ₹96, how much do 6 pens cost? (a) ₹144 (b) ₹168 (c) ₹576 (d) ₹98
24. 24.If 2 mangoes cost ₹10, how much do 5 mangoes cost? (a) ₹30 (b) ₹50 (c) ₹13 (d) ₹25
25. 25.If 6 pens cost ₹108, how much do 12 pens cost? (a) ₹234 (b) ₹216 (c) ₹1296 (d) ₹114
26. 26.If 5 kites cost ₹55, how much do 3 kites cost? (a) ₹165 (b) ₹44 (c) ₹53 (d) ₹33
27. 27.₹112 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹80 (b) ₹16 (c) ₹32 (d) ₹56
28. 28.₹564 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹235 (b) ₹282 (c) ₹47 (d) ₹329
29. 29.If 6 mangoes cost ₹72, how much do 3 mangoes cost? (a) ₹69 (b) ₹48 (c) ₹216 (d) ₹36
30. 30.₹120 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹60 (b) ₹40 (c) ₹80 (d) ₹120
31. 31.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 17 days (c) 5 days (d) 6 days
32. 32.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 11 days (c) 16 days (d) 15 days
33. 33.If 8 pens cost ₹200, how much do 4 pens cost? (a) ₹100 (b) ₹196 (c) ₹800 (d) ₹125
34. 34.If 9 notebooks cost ₹54, how much do 10 notebooks cost? (a) ₹540 (b) ₹66 (c) ₹55 (d) ₹60
35. 35.If 3 pens cost ₹30, how much do 2 pens cost? (a) ₹30 (b) ₹60 (c) ₹20 (d) ₹29
36. 36.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 23 days (d) 22 days
37. 37.₹440 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹220 (b) ₹240 (c) ₹200 (d) ₹40
38. 38.₹162 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹162 (b) ₹27 (c) ₹81 (d) ₹135
39. 39.If 8 kites cost ₹200, how much do 9 kites cost? (a) ₹225 (b) ₹201 (c) ₹250 (d) ₹1800
40. 40.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 3 days (d) 4 days

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