Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 632 · 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 ₹49, how much do 8 pens cost? (a) ₹392 (b) ₹50 (c) ₹56 (d) ₹63
2. 2.If 9 mangoes cost ₹225, how much do 7 mangoes cost? (a) ₹200 (b) ₹1575 (c) ₹223 (d) ₹175
3. 3.₹132 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹36 (b) ₹12 (c) ₹96 (d) ₹66
4. 4.If 9 pens cost ₹45, how much do 2 pens cost? (a) ₹15 (b) ₹38 (c) ₹90 (d) ₹10
5. 5.₹196 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹196 (b) ₹168 (c) ₹28 (d) ₹98
6. 6.₹242 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹44 (b) ₹22 (c) ₹121 (d) ₹198
7. 7.₹550 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹275 (b) ₹300 (c) ₹50 (d) ₹250
8. 8.If 4 pens cost ₹76, how much do 5 pens cost? (a) ₹380 (b) ₹114 (c) ₹95 (d) ₹77
9. 9.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 4 days (d) 2 days
10. 10.₹99 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹55 (b) ₹11 (c) ₹66 (d) ₹44
11. 11.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 14 days (c) 5 days (d) 9 days
12. 12.₹20 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹5 (b) ₹10 (c) ₹15 (d) ₹20
13. 13.If 9 kites cost ₹180, how much do 5 kites cost? (a) ₹176 (b) ₹900 (c) ₹120 (d) ₹100
14. 14.₹310 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹155 (b) ₹93 (c) ₹217 (d) ₹31
15. 15.If 6 pens cost ₹150, how much do 3 pens cost? (a) ₹100 (b) ₹147 (c) ₹75 (d) ₹450
16. 16.₹341 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹248 (b) ₹31 (c) ₹217 (d) ₹124
17. 17.If 3 pens cost ₹24, how much do 4 pens cost? (a) ₹25 (b) ₹32 (c) ₹96 (d) ₹40
18. 18.If 9 pens cost ₹72, how much do 10 pens cost? (a) ₹73 (b) ₹80 (c) ₹88 (d) ₹720
19. 19.₹280 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹140 (b) ₹280 (c) ₹240 (d) ₹40
20. 20.If 3 kites cost ₹66, how much do 2 kites cost? (a) ₹132 (b) ₹44 (c) ₹66 (d) ₹65
21. 21.If 7 mangoes cost ₹42, how much do 8 mangoes cost? (a) ₹336 (b) ₹54 (c) ₹43 (d) ₹48
22. 22.₹473 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹86 (b) ₹43 (c) ₹387 (d) ₹430
23. 23.If 9 kites cost ₹135, how much do 3 kites cost? (a) ₹45 (b) ₹60 (c) ₹405 (d) ₹129
24. 24.If 9 pens cost ₹126, how much do 6 pens cost? (a) ₹756 (b) ₹123 (c) ₹98 (d) ₹84
25. 25.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 8 days (d) 12 days
26. 26.If 4 pens cost ₹52, how much do 6 pens cost? (a) ₹78 (b) ₹54 (c) ₹91 (d) ₹312
27. 27.If 6 kites cost ₹108, how much do 8 kites cost? (a) ₹110 (b) ₹162 (c) ₹144 (d) ₹864
28. 28.₹156 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹13 (b) ₹91 (c) ₹78 (d) ₹65
29. 29.If 4 pens cost ₹88, how much do 5 pens cost? (a) ₹440 (b) ₹89 (c) ₹110 (d) ₹132
30. 30.If 4 pens cost ₹92, how much do 11 pens cost? (a) ₹99 (b) ₹276 (c) ₹1012 (d) ₹253
31. 31.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 11 days (c) 14 days (d) 15 days
32. 32.If 6 notebooks cost ₹30, how much do 3 notebooks cost? (a) ₹20 (b) ₹15 (c) ₹27 (d) ₹90
33. 33.If 2 pens cost ₹24, how much do 10 pens cost? (a) ₹240 (b) ₹32 (c) ₹132 (d) ₹120
34. 34.If 2 mangoes cost ₹6, how much do 12 mangoes cost? (a) ₹36 (b) ₹39 (c) ₹72 (d) ₹16
35. 35.₹429 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹195 (b) ₹234 (c) ₹273 (d) ₹39
36. 36.₹54 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹42 (b) ₹12 (c) ₹6 (d) ₹27
37. 37.If 3 mangoes cost ₹42, how much do 8 mangoes cost? (a) ₹126 (b) ₹112 (c) ₹336 (d) ₹47
38. 38.If 9 kites cost ₹198, how much do 7 kites cost? (a) ₹154 (b) ₹196 (c) ₹176 (d) ₹1386
39. 39.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 3 days (d) 2 days
40. 40.If 8 pens cost ₹24, how much do 9 pens cost? (a) ₹30 (b) ₹216 (c) ₹27 (d) ₹25

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