Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 767 · 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 7 pens cost ₹133, how much do 8 pens cost? (a) ₹171 (b) ₹1064 (c) ₹134 (d) ₹152
2. 2.If 4 mangoes cost ₹28, how much do 3 mangoes cost? (a) ₹27 (b) ₹28 (c) ₹21 (d) ₹84
3. 3.If 8 pens cost ₹32, how much do 6 pens cost? (a) ₹28 (b) ₹24 (c) ₹30 (d) ₹192
4. 4.If 8 notebooks cost ₹32, how much do 11 notebooks cost? (a) ₹352 (b) ₹48 (c) ₹35 (d) ₹44
5. 5.₹120 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹48 (b) ₹72 (c) ₹60 (d) ₹24
6. 6.If 4 pens cost ₹36, how much do 11 pens cost? (a) ₹108 (b) ₹43 (c) ₹99 (d) ₹396
7. 7.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 11 days (d) 2 days
8. 8.₹110 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹60 (b) ₹10 (c) ₹50 (d) ₹55
9. 9.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 24 days (d) 25 days
10. 10.If 6 mangoes cost ₹60, how much do 7 mangoes cost? (a) ₹80 (b) ₹420 (c) ₹61 (d) ₹70
11. 11.₹243 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹135 (b) ₹162 (c) ₹108 (d) ₹27
12. 12.If 9 pens cost ₹72, how much do 3 pens cost? (a) ₹32 (b) ₹216 (c) ₹24 (d) ₹66
13. 13.₹432 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹48 (b) ₹240 (c) ₹192 (d) ₹216
14. 14.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 11 days (c) 8 days (d) 12 days
15. 15.₹266 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹133 (b) ₹76 (c) ₹38 (d) ₹190
16. 16.₹119 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹102 (b) ₹85 (c) ₹17 (d) ₹34
17. 17.If 3 kites cost ₹9, how much do 11 kites cost? (a) ₹36 (b) ₹17 (c) ₹99 (d) ₹33
18. 18.If 9 mangoes cost ₹54, how much do 7 mangoes cost? (a) ₹48 (b) ₹42 (c) ₹378 (d) ₹52
19. 19.If 4 pens cost ₹44, how much do 2 pens cost? (a) ₹33 (b) ₹22 (c) ₹88 (d) ₹42
20. 20.₹42 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹18 (b) ₹24 (c) ₹6 (d) ₹21
21. 21.If 2 kites cost ₹14, how much do 3 kites cost? (a) ₹21 (b) ₹42 (c) ₹28 (d) ₹15
22. 22.If 4 kites cost ₹68, how much do 9 kites cost? (a) ₹170 (b) ₹612 (c) ₹73 (d) ₹153
23. 23.If 4 pens cost ₹40, how much do 6 pens cost? (a) ₹70 (b) ₹240 (c) ₹60 (d) ₹42
24. 24.4 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 14 days (b) 10 days (c) 8 days (d) 18 days
25. 25.9 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 27 days (b) 7 days (c) 28 days (d) 17 days
26. 26.₹126 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹56 (b) ₹63 (c) ₹14 (d) ₹70
27. 27.₹84 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹36 (b) ₹12 (c) ₹48 (d) ₹42
28. 28.If 3 notebooks cost ₹30, how much do 8 notebooks cost? (a) ₹240 (b) ₹80 (c) ₹90 (d) ₹35
29. 29.If 8 kites cost ₹32, how much do 4 kites cost? (a) ₹20 (b) ₹128 (c) ₹28 (d) ₹16
30. 30.₹500 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹50 (b) ₹250 (c) ₹350 (d) ₹150
31. 31.If 9 notebooks cost ₹126, how much do 10 notebooks cost? (a) ₹127 (b) ₹154 (c) ₹1260 (d) ₹140
32. 32.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 21 days (c) 13 days (d) 22 days
33. 33.If 3 mangoes cost ₹54, how much do 9 mangoes cost? (a) ₹180 (b) ₹486 (c) ₹60 (d) ₹162
34. 34.₹135 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹15 (b) ₹75 (c) ₹90 (d) ₹60
35. 35.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 1 day (c) 8 days (d) 10 days
36. 36.If 4 mangoes cost ₹52, how much do 10 mangoes cost? (a) ₹58 (b) ₹520 (c) ₹130 (d) ₹143
37. 37.₹432 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹180 (b) ₹252 (c) ₹216 (d) ₹36
38. 38.₹306 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹34 (b) ₹136 (c) ₹170 (d) ₹153
39. 39.If 7 mangoes cost ₹63, how much do 3 mangoes cost? (a) ₹59 (b) ₹27 (c) ₹36 (d) ₹189
40. 40.If 3 kites cost ₹45, how much do 7 kites cost? (a) ₹120 (b) ₹315 (c) ₹105 (d) ₹49

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