Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 415 · 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.₹50 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹50 (b) ₹25 (c) ₹10 (d) ₹40
2. 2.If 4 kites cost ₹44, how much do 5 kites cost? (a) ₹66 (b) ₹55 (c) ₹45 (d) ₹220
3. 3.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 6 days (d) 5 days
4. 4.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 25 days (b) 4 days (c) 5 days (d) 16 days
5. 5.₹198 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹88 (b) ₹22 (c) ₹110 (d) ₹99
6. 6.If 7 pens cost ₹63, how much do 11 pens cost? (a) ₹693 (b) ₹108 (c) ₹99 (d) ₹67
7. 7.If 6 pens cost ₹138, how much do 7 pens cost? (a) ₹161 (b) ₹184 (c) ₹139 (d) ₹966
8. 8.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 2 days (d) 3 days
9. 9.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 28 days (c) 16 days (d) 12 days
10. 10.If 8 mangoes cost ₹64, how much do 11 mangoes cost? (a) ₹88 (b) ₹67 (c) ₹96 (d) ₹704
11. 11.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 8 days (d) 6 days
12. 12.₹78 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹24 (b) ₹54 (c) ₹39 (d) ₹6
13. 13.If 2 kites cost ₹24, how much do 6 kites cost? (a) ₹144 (b) ₹84 (c) ₹28 (d) ₹72
14. 14.If 2 kites cost ₹26, how much do 3 kites cost? (a) ₹39 (b) ₹78 (c) ₹52 (d) ₹27
15. 15.If 2 notebooks cost ₹36, how much do 12 notebooks cost? (a) ₹216 (b) ₹234 (c) ₹46 (d) ₹432
16. 16.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 49 days (c) 9 days (d) 4 days
17. 17.If 8 kites cost ₹40, how much do 2 kites cost? (a) ₹15 (b) ₹10 (c) ₹34 (d) ₹80
18. 18.If 7 pens cost ₹168, how much do 6 pens cost? (a) ₹167 (b) ₹168 (c) ₹1008 (d) ₹144
19. 19.If 6 pens cost ₹78, how much do 7 pens cost? (a) ₹91 (b) ₹79 (c) ₹104 (d) ₹546
20. 20.₹147 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹21 (b) ₹105 (c) ₹84 (d) ₹63
21. 21.If 6 mangoes cost ₹60, how much do 4 mangoes cost? (a) ₹50 (b) ₹58 (c) ₹40 (d) ₹240
22. 22.₹294 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹42 (b) ₹147 (c) ₹126 (d) ₹168
23. 23.If 3 mangoes cost ₹15, how much do 6 mangoes cost? (a) ₹35 (b) ₹90 (c) ₹18 (d) ₹30
24. 24.If 5 pens cost ₹15, how much do 7 pens cost? (a) ₹105 (b) ₹17 (c) ₹21 (d) ₹24
25. 25.₹96 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹64 (b) ₹96 (c) ₹32 (d) ₹48
26. 26.If 9 notebooks cost ₹135, how much do 7 notebooks cost? (a) ₹105 (b) ₹133 (c) ₹120 (d) ₹945
27. 27.If 8 notebooks cost ₹104, how much do 6 notebooks cost? (a) ₹78 (b) ₹91 (c) ₹102 (d) ₹624
28. 28.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 7 days (d) 1 day
29. 29.If 3 notebooks cost ₹9, how much do 8 notebooks cost? (a) ₹72 (b) ₹14 (c) ₹24 (d) ₹27
30. 30.If 9 mangoes cost ₹207, how much do 12 mangoes cost? (a) ₹299 (b) ₹2484 (c) ₹210 (d) ₹276
31. 31.If 5 mangoes cost ₹80, how much do 8 mangoes cost? (a) ₹128 (b) ₹83 (c) ₹640 (d) ₹144
32. 32.If 9 notebooks cost ₹225, how much do 8 notebooks cost? (a) ₹225 (b) ₹1800 (c) ₹224 (d) ₹200
33. 33.₹182 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹13 (b) ₹65 (c) ₹91 (d) ₹117
34. 34.If 9 pens cost ₹72, how much do 11 pens cost? (a) ₹96 (b) ₹792 (c) ₹88 (d) ₹74
35. 35.If 8 pens cost ₹48, how much do 3 pens cost? (a) ₹144 (b) ₹43 (c) ₹24 (d) ₹18
36. 36.If 2 pens cost ₹40, how much do 12 pens cost? (a) ₹480 (b) ₹240 (c) ₹50 (d) ₹260
37. 37.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 16 days (c) 10 days (d) 17 days
38. 38.If 5 mangoes cost ₹105, how much do 10 mangoes cost? (a) ₹110 (b) ₹1050 (c) ₹231 (d) ₹210
39. 39.₹172 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹172 (b) ₹86 (c) ₹129 (d) ₹43
40. 40.₹36 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹36 (b) ₹18 (c) ₹6 (d) ₹30

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