Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 799 · 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.If 4 pens cost ₹40, how much do 7 pens cost? (a) ₹280 (b) ₹70 (c) ₹80 (d) ₹43
2. 2.₹324 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹162 (b) ₹189 (c) ₹27 (d) ₹135
3. 3.If 6 pens cost ₹66, how much do 4 pens cost? (a) ₹64 (b) ₹44 (c) ₹264 (d) ₹55
4. 4.If 6 kites cost ₹126, how much do 9 kites cost? (a) ₹129 (b) ₹210 (c) ₹1134 (d) ₹189
5. 5.6 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 14 days (b) 16 days (c) 18 days (d) 19 days
6. 6.If 5 mangoes cost ₹60, how much do 6 mangoes cost? (a) ₹84 (b) ₹72 (c) ₹61 (d) ₹360
7. 7.₹325 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹225 (b) ₹100 (c) ₹25 (d) ₹250
8. 8.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 12 days (b) 11 days (c) 3 days (d) 1 day
9. 9.If 8 kites cost ₹112, how much do 2 kites cost? (a) ₹106 (b) ₹224 (c) ₹28 (d) ₹42
10. 10.₹396 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹198 (b) ₹180 (c) ₹36 (d) ₹216
11. 11.₹225 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹200 (b) ₹50 (c) ₹175 (d) ₹25
12. 12.₹55 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹45 (b) ₹40 (c) ₹5 (d) ₹15
13. 13.If 7 mangoes cost ₹98, how much do 6 mangoes cost? (a) ₹84 (b) ₹588 (c) ₹98 (d) ₹97
14. 14.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 16 days (c) 21 days (d) 20 days
15. 15.If 4 notebooks cost ₹72, how much do 5 notebooks cost? (a) ₹73 (b) ₹90 (c) ₹360 (d) ₹108
16. 16.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 15 days (d) 14 days
17. 17.₹192 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹192 (b) ₹160 (c) ₹96 (d) ₹32
18. 18.If 8 mangoes cost ₹104, how much do 11 mangoes cost? (a) ₹143 (b) ₹107 (c) ₹156 (d) ₹1144
19. 19.₹154 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹99 (b) ₹55 (c) ₹11 (d) ₹77
20. 20.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 4 days (d) 17 days
21. 21.₹264 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹132 (b) ₹220 (c) ₹264 (d) ₹44
22. 22.If 5 kites cost ₹110, how much do 4 kites cost? (a) ₹109 (b) ₹440 (c) ₹110 (d) ₹88
23. 23.₹220 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹80 (b) ₹110 (c) ₹20 (d) ₹140
24. 24.If 6 kites cost ₹60, how much do 10 kites cost? (a) ₹110 (b) ₹600 (c) ₹100 (d) ₹64
25. 25.₹119 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹34 (b) ₹102 (c) ₹85 (d) ₹17
26. 26.₹559 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹215 (b) ₹344 (c) ₹43 (d) ₹387
27. 27.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 23 days (b) 14 days (c) 22 days (d) 8 days
28. 28.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 11 days (b) 12 days (c) 18 days (d) 10 days
29. 29.If 4 kites cost ₹72, how much do 7 kites cost? (a) ₹75 (b) ₹504 (c) ₹126 (d) ₹144
30. 30.If 9 pens cost ₹135, how much do 7 pens cost? (a) ₹120 (b) ₹133 (c) ₹105 (d) ₹945
31. 31.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 2 days (d) 8 days
32. 32.If 3 mangoes cost ₹30, how much do 4 mangoes cost? (a) ₹120 (b) ₹31 (c) ₹40 (d) ₹50
33. 33.If 5 notebooks cost ₹55, how much do 11 notebooks cost? (a) ₹61 (b) ₹121 (c) ₹132 (d) ₹605
34. 34.If 5 mangoes cost ₹65, how much do 8 mangoes cost? (a) ₹68 (b) ₹104 (c) ₹520 (d) ₹117
35. 35.₹460 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹230 (b) ₹46 (c) ₹138 (d) ₹322
36. 36.If 3 kites cost ₹66, how much do 11 kites cost? (a) ₹242 (b) ₹264 (c) ₹726 (d) ₹74
37. 37.₹135 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹81 (b) ₹108 (c) ₹54 (d) ₹27
38. 38.₹429 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹264 (b) ₹297 (c) ₹33 (d) ₹165
39. 39.If 4 mangoes cost ₹92, how much do 12 mangoes cost? (a) ₹299 (b) ₹276 (c) ₹100 (d) ₹1104
40. 40.₹168 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹72 (b) ₹24 (c) ₹96 (d) ₹84

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