Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 823 · 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 mangoes cost ₹21, how much do 4 mangoes cost? (a) ₹18 (b) ₹84 (c) ₹15 (d) ₹12
2. 2.If 3 kites cost ₹24, how much do 4 kites cost? (a) ₹32 (b) ₹40 (c) ₹96 (d) ₹25
3. 3.If 8 pens cost ₹64, how much do 5 pens cost? (a) ₹320 (b) ₹48 (c) ₹40 (d) ₹61
4. 4.₹350 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹300 (b) ₹350 (c) ₹175 (d) ₹50
5. 5.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 15 days (d) 16 days
6. 6.If 2 notebooks cost ₹26, how much do 8 notebooks cost? (a) ₹208 (b) ₹32 (c) ₹104 (d) ₹117
7. 7.₹198 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹198 (b) ₹176 (c) ₹22 (d) ₹99
8. 8.₹644 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹230 (b) ₹46 (c) ₹322 (d) ₹414
9. 9.₹280 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹200 (b) ₹80 (c) ₹140 (d) ₹40
10. 10.₹351 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹156 (b) ₹195 (c) ₹234 (d) ₹39
11. 11.If 2 pens cost ₹12, how much do 7 pens cost? (a) ₹84 (b) ₹42 (c) ₹48 (d) ₹17
12. 12.If 4 kites cost ₹40, how much do 5 kites cost? (a) ₹200 (b) ₹41 (c) ₹60 (d) ₹50
13. 13.If 2 notebooks cost ₹28, how much do 10 notebooks cost? (a) ₹140 (b) ₹36 (c) ₹280 (d) ₹154
14. 14.If 8 pens cost ₹56, how much do 5 pens cost? (a) ₹42 (b) ₹35 (c) ₹53 (d) ₹280
15. 15.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 9 days (d) 7 days
16. 16.If 2 pens cost ₹46, how much do 3 pens cost? (a) ₹47 (b) ₹138 (c) ₹92 (d) ₹69
17. 17.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 1 day (c) 11 days (d) 10 days
18. 18.₹169 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹65 (b) ₹117 (c) ₹13 (d) ₹104
19. 19.If 8 notebooks cost ₹72, how much do 11 notebooks cost? (a) ₹99 (b) ₹792 (c) ₹75 (d) ₹108
20. 20.₹153 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹34 (b) ₹136 (c) ₹119 (d) ₹17
21. 21.If 8 mangoes cost ₹56, how much do 6 mangoes cost? (a) ₹42 (b) ₹49 (c) ₹54 (d) ₹336
22. 22.If 8 pens cost ₹72, how much do 2 pens cost? (a) ₹66 (b) ₹27 (c) ₹18 (d) ₹144
23. 23.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 5 days (c) 11 days (d) 19 days
24. 24.If 8 kites cost ₹120, how much do 11 kites cost? (a) ₹123 (b) ₹1320 (c) ₹165 (d) ₹180
25. 25.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 6 days (d) 7 days
26. 26.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 14 days (b) 5 days (c) 20 days (d) 6 days
27. 27.If 2 notebooks cost ₹28, how much do 6 notebooks cost? (a) ₹98 (b) ₹84 (c) ₹32 (d) ₹168
28. 28.If 3 mangoes cost ₹18, how much do 9 mangoes cost? (a) ₹54 (b) ₹60 (c) ₹162 (d) ₹24
29. 29.If 9 kites cost ₹225, how much do 7 kites cost? (a) ₹200 (b) ₹223 (c) ₹1575 (d) ₹175
30. 30.₹60 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹60 (b) ₹30 (c) ₹45 (d) ₹15
31. 31.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 11 days (c) 19 days (d) 7 days
32. 32.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 26 days (c) 28 days (d) 13 days
33. 33.₹65 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹5 (b) ₹40 (c) ₹25 (d) ₹45
34. 34.₹132 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹66 (b) ₹108 (c) ₹12 (d) ₹24
35. 35.If 7 notebooks cost ₹28, how much do 6 notebooks cost? (a) ₹28 (b) ₹24 (c) ₹27 (d) ₹168
36. 36.₹192 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹16 (b) ₹80 (c) ₹96 (d) ₹112
37. 37.If 6 notebooks cost ₹132, how much do 4 notebooks cost? (a) ₹110 (b) ₹88 (c) ₹528 (d) ₹130
38. 38.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 9 days (d) 10 days
39. 39.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 14 days (d) 3 days
40. 40.₹108 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹54 (b) ₹27 (c) ₹108 (d) ₹81

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