Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 198 · 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 9 kites cost ₹207, how much do 5 kites cost? (a) ₹1035 (b) ₹115 (c) ₹203 (d) ₹138
2. 2.If 5 pens cost ₹120, how much do 10 pens cost? (a) ₹240 (b) ₹264 (c) ₹1200 (d) ₹125
3. 3.₹528 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹48 (b) ₹240 (c) ₹264 (d) ₹288
4. 4.If 7 mangoes cost ₹49, how much do 3 mangoes cost? (a) ₹147 (b) ₹45 (c) ₹28 (d) ₹21
5. 5.If 9 kites cost ₹63, how much do 5 kites cost? (a) ₹42 (b) ₹315 (c) ₹35 (d) ₹59
6. 6.₹111 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹111 (b) ₹37 (c) ₹74 (d) ₹75
7. 7.₹290 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹290 (b) ₹261 (c) ₹145 (d) ₹29
8. 8.If 2 pens cost ₹14, how much do 4 pens cost? (a) ₹28 (b) ₹35 (c) ₹56 (d) ₹16
9. 9.₹99 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹55 (b) ₹44 (c) ₹11 (d) ₹66
10. 10.If 7 pens cost ₹112, how much do 4 pens cost? (a) ₹109 (b) ₹448 (c) ₹80 (d) ₹64
11. 11.If 6 pens cost ₹48, how much do 8 pens cost? (a) ₹50 (b) ₹64 (c) ₹72 (d) ₹384
12. 12.₹416 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹288 (b) ₹128 (c) ₹32 (d) ₹208
13. 13.If 5 kites cost ₹120, how much do 10 kites cost? (a) ₹1200 (b) ₹240 (c) ₹125 (d) ₹264
14. 14.9 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
15. 15.₹91 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹13 (b) ₹39 (c) ₹52 (d) ₹65
16. 16.If 5 pens cost ₹115, how much do 6 pens cost? (a) ₹690 (b) ₹116 (c) ₹161 (d) ₹138
17. 17.If 4 pens cost ₹28, how much do 9 pens cost? (a) ₹252 (b) ₹33 (c) ₹70 (d) ₹63
18. 18.₹504 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹210 (b) ₹294 (c) ₹42 (d) ₹252
19. 19.If 2 pens cost ₹38, how much do 9 pens cost? (a) ₹190 (b) ₹342 (c) ₹45 (d) ₹171
20. 20.₹306 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹170 (b) ₹34 (c) ₹153 (d) ₹136
21. 21.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 2 days (c) 3 days (d) 4 days
22. 22.If 4 mangoes cost ₹48, how much do 12 mangoes cost? (a) ₹56 (b) ₹576 (c) ₹156 (d) ₹144
23. 23.₹203 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹116 (b) ₹29 (c) ₹145 (d) ₹87
24. 24.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 6 days (d) 2 days
25. 25.9 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 14 days (b) 6 days (c) 19 days (d) 18 days
26. 26.If 2 pens cost ₹20, how much do 8 pens cost? (a) ₹80 (b) ₹90 (c) ₹26 (d) ₹160
27. 27.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 40 days (c) 7 days (d) 19 days
28. 28.₹407 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹74 (b) ₹37 (c) ₹333 (d) ₹370
29. 29.₹384 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹160 (b) ₹32 (c) ₹224 (d) ₹192
30. 30.If 3 kites cost ₹72, how much do 6 kites cost? (a) ₹168 (b) ₹75 (c) ₹144 (d) ₹432
31. 31.If 2 notebooks cost ₹16, how much do 3 notebooks cost? (a) ₹17 (b) ₹32 (c) ₹24 (d) ₹48
32. 32.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 18 days (c) 7 days (d) 10 days
33. 33.₹198 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹22 (b) ₹198 (c) ₹99 (d) ₹176
34. 34.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 11 days (d) 26 days
35. 35.If 4 mangoes cost ₹44, how much do 6 mangoes cost? (a) ₹46 (b) ₹77 (c) ₹66 (d) ₹264
36. 36.₹256 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹128 (b) ₹224 (c) ₹256 (d) ₹32
37. 37.If 3 mangoes cost ₹9, how much do 4 mangoes cost? (a) ₹36 (b) ₹10 (c) ₹15 (d) ₹12
38. 38.If 8 mangoes cost ₹64, how much do 9 mangoes cost? (a) ₹65 (b) ₹80 (c) ₹72 (d) ₹576
39. 39.If 9 kites cost ₹72, how much do 12 kites cost? (a) ₹96 (b) ₹75 (c) ₹104 (d) ₹864
40. 40.₹220 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹44 (b) ₹132 (c) ₹88 (d) ₹110

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