Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 719 · 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 6 pens cost ₹102, how much do 7 pens cost? (a) ₹119 (b) ₹136 (c) ₹103 (d) ₹714
2. 2.If 6 kites cost ₹78, how much do 9 kites cost? (a) ₹130 (b) ₹702 (c) ₹117 (d) ₹81
3. 3.If 9 pens cost ₹27, how much do 6 pens cost? (a) ₹24 (b) ₹162 (c) ₹21 (d) ₹18
4. 4.If 9 mangoes cost ₹171, how much do 10 mangoes cost? (a) ₹190 (b) ₹172 (c) ₹1710 (d) ₹209
5. 5.If 7 pens cost ₹42, how much do 2 pens cost? (a) ₹37 (b) ₹84 (c) ₹18 (d) ₹12
6. 6.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 18 days (d) 15 days
7. 7.If 9 pens cost ₹189, how much do 8 pens cost? (a) ₹168 (b) ₹189 (c) ₹188 (d) ₹1512
8. 8.If 2 pens cost ₹8, how much do 12 pens cost? (a) ₹52 (b) ₹96 (c) ₹48 (d) ₹18
9. 9.If 3 notebooks cost ₹42, how much do 4 notebooks cost? (a) ₹168 (b) ₹43 (c) ₹70 (d) ₹56
10. 10.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 2 days (c) 15 days (d) 14 days
11. 11.₹64 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹64 (b) ₹32 (c) ₹48 (d) ₹16
12. 12.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 28 days (c) 29 days (d) 1 day
13. 13.If 3 kites cost ₹12, how much do 4 kites cost? (a) ₹20 (b) ₹13 (c) ₹16 (d) ₹48
14. 14.₹304 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹152 (b) ₹38 (c) ₹190 (d) ₹114
15. 15.If 4 mangoes cost ₹48, how much do 6 mangoes cost? (a) ₹84 (b) ₹50 (c) ₹288 (d) ₹72
16. 16.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 28 days (c) 15 days (d) 27 days
17. 17.₹56 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹56 (b) ₹14 (c) ₹28 (d) ₹42
18. 18.If 8 kites cost ₹32, how much do 10 kites cost? (a) ₹44 (b) ₹40 (c) ₹320 (d) ₹34
19. 19.If 8 kites cost ₹88, how much do 9 kites cost? (a) ₹99 (b) ₹792 (c) ₹89 (d) ₹110
20. 20.If 8 notebooks cost ₹32, how much do 12 notebooks cost? (a) ₹384 (b) ₹48 (c) ₹52 (d) ₹36
21. 21.If 5 mangoes cost ₹40, how much do 2 mangoes cost? (a) ₹16 (b) ₹24 (c) ₹37 (d) ₹80
22. 22.If 6 notebooks cost ₹54, how much do 7 notebooks cost? (a) ₹72 (b) ₹378 (c) ₹55 (d) ₹63
23. 23.If 2 mangoes cost ₹24, how much do 3 mangoes cost? (a) ₹72 (b) ₹36 (c) ₹25 (d) ₹48
24. 24.If 2 mangoes cost ₹22, how much do 8 mangoes cost? (a) ₹28 (b) ₹88 (c) ₹176 (d) ₹99
25. 25.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 9 days (d) 7 days
26. 26.If 2 kites cost ₹8, how much do 3 kites cost? (a) ₹12 (b) ₹16 (c) ₹9 (d) ₹24
27. 27.₹574 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹41 (b) ₹369 (c) ₹205 (d) ₹287
28. 28.8 workers can build a wall in 9 days. How many days will 4 workers take, working at the same speed? (a) 18 days (b) 19 days (c) 5 days (d) 13 days
29. 29.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 1 day (d) 2 days
30. 30.₹176 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹88 (b) ₹48 (c) ₹128 (d) ₹16
31. 31.₹165 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹90 (b) ₹105 (c) ₹75 (d) ₹15
32. 32.₹164 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹41 (b) ₹164 (c) ₹82 (d) ₹123
33. 33.If 9 kites cost ₹36, how much do 6 kites cost? (a) ₹33 (b) ₹28 (c) ₹24 (d) ₹216
34. 34.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 15 days
35. 35.₹481 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹333 (b) ₹37 (c) ₹185 (d) ₹296
36. 36.₹432 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹48 (b) ₹96 (c) ₹216 (d) ₹336
37. 37.If 8 mangoes cost ₹88, how much do 6 mangoes cost? (a) ₹66 (b) ₹528 (c) ₹77 (d) ₹86
38. 38.9 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 8 days (d) 9 days
39. 39.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 37 days (d) 36 days
40. 40.If 8 mangoes cost ₹120, how much do 2 mangoes cost? (a) ₹240 (b) ₹45 (c) ₹114 (d) ₹30

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