Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 78 · 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. 1.6 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 20 days (d) 13 days
2. 2.₹99 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹90 (b) ₹9 (c) ₹81 (d) ₹18
3. 3.If 7 kites cost ₹77, how much do 5 kites cost? (a) ₹66 (b) ₹75 (c) ₹385 (d) ₹55
4. 4.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 9 days (d) 5 days
5. 5.If 7 notebooks cost ₹56, how much do 3 notebooks cost? (a) ₹52 (b) ₹32 (c) ₹168 (d) ₹24
6. 6.₹216 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹96 (b) ₹120 (c) ₹108 (d) ₹24
7. 7.4 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 12 days (d) 13 days
8. 8.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 7 days (d) 3 days
9. 9.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 15 days (d) 11 days
10. 10.If 4 pens cost ₹24, how much do 5 pens cost? (a) ₹25 (b) ₹30 (c) ₹36 (d) ₹120
11. 11.₹70 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹14 (b) ₹42 (c) ₹35 (d) ₹28
12. 12.₹132 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹66 (b) ₹12 (c) ₹36 (d) ₹96
13. 13.₹144 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹96 (b) ₹72 (c) ₹144 (d) ₹48
14. 14.If 9 notebooks cost ₹225, how much do 5 notebooks cost? (a) ₹221 (b) ₹150 (c) ₹125 (d) ₹1125
15. 15.If 7 notebooks cost ₹91, how much do 2 notebooks cost? (a) ₹182 (b) ₹26 (c) ₹86 (d) ₹39
16. 16.If 7 mangoes cost ₹154, how much do 5 mangoes cost? (a) ₹110 (b) ₹770 (c) ₹152 (d) ₹132
17. 17.₹231 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹198 (b) ₹66 (c) ₹165 (d) ₹33
18. 18.If 2 kites cost ₹34, how much do 8 kites cost? (a) ₹272 (b) ₹136 (c) ₹153 (d) ₹40
19. 19.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 14 days (b) 18 days (c) 3 days (d) 2 days
20. 20.If 9 kites cost ₹198, how much do 11 kites cost? (a) ₹200 (b) ₹242 (c) ₹264 (d) ₹2178
21. 21.₹440 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹200 (b) ₹40 (c) ₹240 (d) ₹220
22. 22.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 11 days (c) 16 days (d) 7 days
23. 23.If 6 kites cost ₹24, how much do 2 kites cost? (a) ₹8 (b) ₹20 (c) ₹48 (d) ₹12
24. 24.If 4 mangoes cost ₹36, how much do 5 mangoes cost? (a) ₹180 (b) ₹37 (c) ₹45 (d) ₹54
25. 25.If 9 pens cost ₹63, how much do 5 pens cost? (a) ₹35 (b) ₹42 (c) ₹315 (d) ₹59
26. 26.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 7 days (d) 4 days
27. 27.₹264 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹44 (b) ₹132 (c) ₹264 (d) ₹220
28. 28.If 7 kites cost ₹49, how much do 2 kites cost? (a) ₹21 (b) ₹44 (c) ₹98 (d) ₹14
29. 29.If 5 mangoes cost ₹125, how much do 12 mangoes cost? (a) ₹1500 (b) ₹325 (c) ₹132 (d) ₹300
30. 30.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 43 days (b) 7 days (c) 42 days (d) 17 days
31. 31.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 63 days (b) 21 days (c) 7 days (d) 64 days
32. 32.If 4 kites cost ₹16, how much do 7 kites cost? (a) ₹112 (b) ₹32 (c) ₹28 (d) ₹19
33. 33.If 3 notebooks cost ₹69, how much do 7 notebooks cost? (a) ₹184 (b) ₹483 (c) ₹73 (d) ₹161
34. 34.₹315 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹210 (b) ₹175 (c) ₹140 (d) ₹35
35. 35.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 34 days (b) 17 days (c) 33 days (d) 5 days
36. 36.₹546 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹273 (b) ₹39 (c) ₹351 (d) ₹195
37. 37.If 9 mangoes cost ₹27, how much do 10 mangoes cost? (a) ₹270 (b) ₹28 (c) ₹33 (d) ₹30
38. 38.If 6 mangoes cost ₹138, how much do 4 mangoes cost? (a) ₹552 (b) ₹115 (c) ₹136 (d) ₹92
39. 39.₹338 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹169 (b) ₹26 (c) ₹104 (d) ₹234
40. 40.If 9 notebooks cost ₹171, how much do 7 notebooks cost? (a) ₹152 (b) ₹169 (c) ₹133 (d) ₹1197

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