Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 717 · 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.₹243 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹162 (b) ₹108 (c) ₹27 (d) ₹135
2. 2.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 52 days (b) 7 days (c) 19 days (d) 53 days
3. 3.If 4 notebooks cost ₹44, how much do 2 notebooks cost? (a) ₹88 (b) ₹42 (c) ₹22 (d) ₹33
4. 4.If 4 mangoes cost ₹100, how much do 5 mangoes cost? (a) ₹125 (b) ₹150 (c) ₹101 (d) ₹500
5. 5.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 14 days (d) 15 days
6. 6.If 9 mangoes cost ₹198, how much do 7 mangoes cost? (a) ₹196 (b) ₹154 (c) ₹176 (d) ₹1386
7. 7.If 3 pens cost ₹72, how much do 12 pens cost? (a) ₹312 (b) ₹288 (c) ₹81 (d) ₹864
8. 8.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 18 days (b) 7 days (c) 10 days (d) 28 days
9. 9.If 3 notebooks cost ₹15, how much do 2 notebooks cost? (a) ₹14 (b) ₹10 (c) ₹30 (d) ₹15
10. 10.₹40 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹40 (b) ₹10 (c) ₹30 (d) ₹20
11. 11.If 9 mangoes cost ₹27, how much do 4 mangoes cost? (a) ₹108 (b) ₹12 (c) ₹15 (d) ₹22
12. 12.If 2 mangoes cost ₹8, how much do 7 mangoes cost? (a) ₹13 (b) ₹32 (c) ₹56 (d) ₹28
13. 13.If 2 pens cost ₹16, how much do 8 pens cost? (a) ₹72 (b) ₹64 (c) ₹128 (d) ₹22
14. 14.If 7 notebooks cost ₹91, how much do 10 notebooks cost? (a) ₹910 (b) ₹143 (c) ₹130 (d) ₹94
15. 15.₹176 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹44 (b) ₹88 (c) ₹176 (d) ₹132
16. 16.₹192 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹192 (b) ₹96 (c) ₹168 (d) ₹24
17. 17.If 3 kites cost ₹48, how much do 7 kites cost? (a) ₹128 (b) ₹112 (c) ₹52 (d) ₹336
18. 18.If 4 mangoes cost ₹16, how much do 8 mangoes cost? (a) ₹20 (b) ₹128 (c) ₹36 (d) ₹32
19. 19.₹104 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹52 (b) ₹65 (c) ₹39 (d) ₹13
20. 20.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 3 days (c) 28 days (d) 15 days
21. 21.If 6 mangoes cost ₹114, how much do 8 mangoes cost? (a) ₹912 (b) ₹171 (c) ₹152 (d) ₹116
22. 22.₹205 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹41 (b) ₹165 (c) ₹205 (d) ₹164
23. 23.If 3 notebooks cost ₹12, how much do 10 notebooks cost? (a) ₹40 (b) ₹19 (c) ₹120 (d) ₹44
24. 24.If 9 pens cost ₹108, how much do 5 pens cost? (a) ₹72 (b) ₹104 (c) ₹60 (d) ₹540
25. 25.If 2 mangoes cost ₹46, how much do 9 mangoes cost? (a) ₹230 (b) ₹414 (c) ₹207 (d) ₹53
26. 26.If 7 kites cost ₹21, how much do 11 kites cost? (a) ₹231 (b) ₹36 (c) ₹33 (d) ₹25
27. 27.If 7 notebooks cost ₹112, how much do 2 notebooks cost? (a) ₹32 (b) ₹107 (c) ₹224 (d) ₹48
28. 28.If 6 pens cost ₹126, how much do 4 pens cost? (a) ₹84 (b) ₹124 (c) ₹504 (d) ₹105
29. 29.₹328 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹41 (b) ₹328 (c) ₹287 (d) ₹164
30. 30.₹63 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹54 (b) ₹55 (c) ₹63 (d) ₹9
31. 31.₹132 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹55 (b) ₹11 (c) ₹77 (d) ₹66
32. 32.If 3 notebooks cost ₹27, how much do 7 notebooks cost? (a) ₹31 (b) ₹72 (c) ₹63 (d) ₹189
33. 33.If 5 pens cost ₹45, how much do 9 pens cost? (a) ₹90 (b) ₹405 (c) ₹49 (d) ₹81
34. 34.₹60 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹54 (b) ₹60 (c) ₹30 (d) ₹6
35. 35.₹351 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹195 (b) ₹39 (c) ₹234 (d) ₹156
36. 36.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 35 days (b) 36 days (c) 11 days (d) 19 days
37. 37.₹336 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹336 (b) ₹48 (c) ₹168 (d) ₹288
38. 38.If 2 notebooks cost ₹16, how much do 3 notebooks cost? (a) ₹32 (b) ₹48 (c) ₹17 (d) ₹24
39. 39.If 4 notebooks cost ₹60, how much do 3 notebooks cost? (a) ₹45 (b) ₹180 (c) ₹59 (d) ₹60
40. 40.₹322 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹23 (b) ₹207 (c) ₹161 (d) ₹115

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