Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 493 · 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 notebooks cost ₹98, how much do 12 notebooks cost? (a) ₹1176 (b) ₹168 (c) ₹103 (d) ₹182
2. 2.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 13 days (b) 1 day (c) 2 days (d) 16 days
3. 3.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 6 days (d) 16 days
4. 4.₹418 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹209 (b) ₹266 (c) ₹152 (d) ₹38
5. 5.8 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 16 days (d) 7 days
6. 6.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 22 days (d) 21 days
7. 7.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 19 days (c) 4 days (d) 2 days
8. 8.If 7 pens cost ₹70, how much do 2 pens cost? (a) ₹65 (b) ₹30 (c) ₹20 (d) ₹140
9. 9.If 2 notebooks cost ₹18, how much do 11 notebooks cost? (a) ₹198 (b) ₹99 (c) ₹27 (d) ₹108
10. 10.If 3 kites cost ₹18, how much do 4 kites cost? (a) ₹72 (b) ₹19 (c) ₹30 (d) ₹24
11. 11.If 7 pens cost ₹49, how much do 8 pens cost? (a) ₹63 (b) ₹392 (c) ₹56 (d) ₹50
12. 12.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 7 days (d) 2 days
13. 13.₹189 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹135 (b) ₹27 (c) ₹162 (d) ₹54
14. 14.₹170 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹51 (b) ₹17 (c) ₹85 (d) ₹119
15. 15.If 8 mangoes cost ₹200, how much do 6 mangoes cost? (a) ₹1200 (b) ₹198 (c) ₹175 (d) ₹150
16. 16.If 4 kites cost ₹68, how much do 5 kites cost? (a) ₹85 (b) ₹102 (c) ₹340 (d) ₹69
17. 17.If 8 notebooks cost ₹128, how much do 6 notebooks cost? (a) ₹126 (b) ₹96 (c) ₹768 (d) ₹112
18. 18.If 5 kites cost ₹20, how much do 4 kites cost? (a) ₹19 (b) ₹16 (c) ₹80 (d) ₹20
19. 19.₹115 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹46 (b) ₹92 (c) ₹69 (d) ₹23
20. 20.If 7 notebooks cost ₹77, how much do 3 notebooks cost? (a) ₹33 (b) ₹73 (c) ₹44 (d) ₹231
21. 21.If 3 notebooks cost ₹15, how much do 4 notebooks cost? (a) ₹16 (b) ₹25 (c) ₹20 (d) ₹60
22. 22.If 3 pens cost ₹45, how much do 6 pens cost? (a) ₹105 (b) ₹48 (c) ₹270 (d) ₹90
23. 23.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 21 days (c) 16 days (d) 20 days
24. 24.If 7 pens cost ₹126, how much do 8 pens cost? (a) ₹144 (b) ₹162 (c) ₹1008 (d) ₹127
25. 25.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 2 days (c) 19 days (d) 18 days
26. 26.₹176 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹22 (b) ₹176 (c) ₹88 (d) ₹154
27. 27.₹448 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹32 (b) ₹160 (c) ₹224 (d) ₹288
28. 28.₹182 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹70 (b) ₹14 (c) ₹91 (d) ₹112
29. 29.₹258 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹43 (b) ₹129 (c) ₹258 (d) ₹215
30. 30.If 5 mangoes cost ₹75, how much do 6 mangoes cost? (a) ₹90 (b) ₹450 (c) ₹105 (d) ₹76
31. 31.If 5 mangoes cost ₹25, how much do 2 mangoes cost? (a) ₹50 (b) ₹15 (c) ₹22 (d) ₹10
32. 32.If 4 kites cost ₹20, how much do 6 kites cost? (a) ₹35 (b) ₹30 (c) ₹120 (d) ₹22
33. 33.₹468 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹195 (b) ₹234 (c) ₹39 (d) ₹273
34. 34.₹252 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹105 (b) ₹21 (c) ₹147 (d) ₹126
35. 35.If 2 kites cost ₹26, how much do 7 kites cost? (a) ₹182 (b) ₹91 (c) ₹104 (d) ₹31
36. 36.₹550 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹275 (b) ₹250 (c) ₹50 (d) ₹300
37. 37.If 6 mangoes cost ₹72, how much do 2 mangoes cost? (a) ₹68 (b) ₹24 (c) ₹36 (d) ₹144
38. 38.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 11 days (d) 6 days
39. 39.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 8 days (c) 10 days (d) 9 days
40. 40.₹85 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹34 (b) ₹68 (c) ₹17 (d) ₹51

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