Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 322 · 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. 1.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 1 day (d) 3 days
2. 2.If 9 pens cost ₹108, how much do 5 pens cost? (a) ₹104 (b) ₹540 (c) ₹72 (d) ₹60
3. 3.If 6 mangoes cost ₹42, how much do 7 mangoes cost? (a) ₹43 (b) ₹49 (c) ₹294 (d) ₹56
4. 4.If 7 pens cost ₹168, how much do 8 pens cost? (a) ₹216 (b) ₹1344 (c) ₹192 (d) ₹169
5. 5.If 2 notebooks cost ₹34, how much do 8 notebooks cost? (a) ₹272 (b) ₹153 (c) ₹136 (d) ₹40
6. 6.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 15 days (d) 13 days
7. 7.If 5 mangoes cost ₹85, how much do 2 mangoes cost? (a) ₹170 (b) ₹34 (c) ₹51 (d) ₹82
8. 8.₹441 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹196 (b) ₹294 (c) ₹245 (d) ₹49
9. 9.₹533 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹41 (b) ₹205 (c) ₹369 (d) ₹328
10. 10.If 8 kites cost ₹136, how much do 10 kites cost? (a) ₹170 (b) ₹187 (c) ₹138 (d) ₹1360
11. 11.₹117 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹72 (b) ₹9 (c) ₹45 (d) ₹81
12. 12.₹208 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹144 (b) ₹64 (c) ₹16 (d) ₹104
13. 13.If 3 mangoes cost ₹21, how much do 2 mangoes cost? (a) ₹42 (b) ₹21 (c) ₹20 (d) ₹14
14. 14.If 2 mangoes cost ₹8, how much do 3 mangoes cost? (a) ₹9 (b) ₹16 (c) ₹24 (d) ₹12
15. 15.₹110 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹50 (b) ₹10 (c) ₹55 (d) ₹60
16. 16.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 26 days (c) 10 days (d) 27 days
17. 17.₹231 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹189 (b) ₹21 (c) ₹63 (d) ₹168
18. 18.₹252 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹105 (b) ₹126 (c) ₹147 (d) ₹21
19. 19.If 6 notebooks cost ₹24, how much do 3 notebooks cost? (a) ₹21 (b) ₹72 (c) ₹12 (d) ₹16
20. 20.₹98 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹28 (b) ₹70 (c) ₹49 (d) ₹14
21. 21.9 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 9 days (d) 7 days
22. 22.₹33 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹22 (b) ₹23 (c) ₹33 (d) ₹11
23. 23.₹494 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹247 (b) ₹152 (c) ₹38 (d) ₹342
24. 24.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 13 days (d) 3 days
25. 25.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 5 days (c) 13 days (d) 22 days
26. 26.If 8 pens cost ₹200, how much do 3 pens cost? (a) ₹195 (b) ₹100 (c) ₹75 (d) ₹600
27. 27.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 1 day (c) 16 days (d) 17 days
28. 28.₹176 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹88 (b) ₹176 (c) ₹132 (d) ₹44
29. 29.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 6 days (d) 4 days
30. 30.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 12 days
31. 31.₹440 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹40 (b) ₹220 (c) ₹200 (d) ₹240
32. 32.₹48 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹6 (b) ₹18 (c) ₹24 (d) ₹30
33. 33.₹308 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹252 (b) ₹56 (c) ₹154 (d) ₹28
34. 34.If 7 kites cost ₹77, how much do 8 kites cost? (a) ₹78 (b) ₹88 (c) ₹99 (d) ₹616
35. 35.If 3 pens cost ₹60, how much do 6 pens cost? (a) ₹63 (b) ₹360 (c) ₹140 (d) ₹120
36. 36.₹72 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹40 (b) ₹8 (c) ₹32 (d) ₹36
37. 37.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 13 days (c) 3 days (d) 29 days
38. 38.If 7 pens cost ₹98, how much do 8 pens cost? (a) ₹112 (b) ₹784 (c) ₹99 (d) ₹126
39. 39.If 7 notebooks cost ₹105, how much do 4 notebooks cost? (a) ₹102 (b) ₹420 (c) ₹75 (d) ₹60
40. 40.If 5 pens cost ₹110, how much do 7 pens cost? (a) ₹176 (b) ₹112 (c) ₹770 (d) ₹154

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