Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 923 · 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.₹350 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹150 (b) ₹50 (c) ₹175 (d) ₹200
2. 2.If 2 mangoes cost ₹16, how much do 3 mangoes cost? (a) ₹17 (b) ₹48 (c) ₹24 (d) ₹32
3. 3.₹130 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹10 (b) ₹90 (c) ₹65 (d) ₹40
4. 4.₹396 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹36 (b) ₹198 (c) ₹288 (d) ₹108
5. 5.₹175 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹140 (b) ₹141 (c) ₹175 (d) ₹35
6. 6.₹360 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹36 (b) ₹252 (c) ₹108 (d) ₹180
7. 7.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 21 days (c) 9 days (d) 45 days
8. 8.If 3 kites cost ₹60, how much do 12 kites cost? (a) ₹260 (b) ₹69 (c) ₹240 (d) ₹720
9. 9.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 28 days (c) 3 days (d) 15 days
10. 10.₹50 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹15 (b) ₹25 (c) ₹5 (d) ₹35
11. 11.If 2 mangoes cost ₹12, how much do 3 mangoes cost? (a) ₹36 (b) ₹24 (c) ₹18 (d) ₹13
12. 12.If 9 pens cost ₹54, how much do 11 pens cost? (a) ₹72 (b) ₹56 (c) ₹66 (d) ₹594
13. 13.If 4 notebooks cost ₹28, how much do 2 notebooks cost? (a) ₹21 (b) ₹26 (c) ₹14 (d) ₹56
14. 14.If 8 pens cost ₹104, how much do 7 pens cost? (a) ₹103 (b) ₹91 (c) ₹104 (d) ₹728
15. 15.₹410 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹205 (b) ₹410 (c) ₹41 (d) ₹369
16. 16.If 4 pens cost ₹44, how much do 12 pens cost? (a) ₹528 (b) ₹143 (c) ₹132 (d) ₹52
17. 17.₹187 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹17 (b) ₹51 (c) ₹153 (d) ₹136
18. 18.₹336 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹42 (b) ₹168 (c) ₹336 (d) ₹294
19. 19.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 7 days
20. 20.₹392 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹140 (b) ₹196 (c) ₹28 (d) ₹252
21. 21.₹440 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹132 (b) ₹220 (c) ₹308 (d) ₹44
22. 22.If 6 mangoes cost ₹90, how much do 5 mangoes cost? (a) ₹450 (b) ₹90 (c) ₹89 (d) ₹75
23. 23.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 27 days (b) 28 days (c) 11 days (d) 19 days
24. 24.If 8 mangoes cost ₹176, how much do 5 mangoes cost? (a) ₹132 (b) ₹110 (c) ₹880 (d) ₹173
25. 25.If 2 mangoes cost ₹22, how much do 12 mangoes cost? (a) ₹32 (b) ₹264 (c) ₹143 (d) ₹132
26. 26.₹420 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹270 (b) ₹150 (c) ₹210 (d) ₹30
27. 27.If 9 mangoes cost ₹45, how much do 2 mangoes cost? (a) ₹38 (b) ₹15 (c) ₹90 (d) ₹10
28. 28.8 workers can build a wall in 9 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 18 days (c) 19 days (d) 13 days
29. 29.If 6 kites cost ₹96, how much do 2 kites cost? (a) ₹48 (b) ₹92 (c) ₹32 (d) ₹192
30. 30.₹104 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹8 (b) ₹52 (c) ₹40 (d) ₹64
31. 31.₹360 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹320 (b) ₹180 (c) ₹360 (d) ₹40
32. 32.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 24 days (c) 9 days (d) 6 days
33. 33.₹533 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹164 (b) ₹369 (c) ₹41 (d) ₹410
34. 34.If 4 notebooks cost ₹12, how much do 9 notebooks cost? (a) ₹17 (b) ₹30 (c) ₹27 (d) ₹108
35. 35.If 9 mangoes cost ₹171, how much do 7 mangoes cost? (a) ₹1197 (b) ₹169 (c) ₹152 (d) ₹133
36. 36.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 11 days (d) 8 days
37. 37.₹273 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹234 (b) ₹273 (c) ₹39 (d) ₹235
38. 38.4 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
39. 39.₹280 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹40 (b) ₹140 (c) ₹240 (d) ₹280
40. 40.If 2 notebooks cost ₹14, how much do 11 notebooks cost? (a) ₹23 (b) ₹154 (c) ₹77 (d) ₹84

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