Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 374 · 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 2 mangoes cost ₹20, how much do 7 mangoes cost? (a) ₹25 (b) ₹140 (c) ₹80 (d) ₹70
2. 2.₹270 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹243 (b) ₹270 (c) ₹135 (d) ₹27
3. 3.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 28 days (d) 18 days
4. 4.If 7 pens cost ₹161, how much do 3 pens cost? (a) ₹483 (b) ₹157 (c) ₹92 (d) ₹69
5. 5.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 19 days (c) 21 days (d) 11 days
6. 6.₹207 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹23 (b) ₹115 (c) ₹138 (d) ₹92
7. 7.If 2 pens cost ₹40, how much do 9 pens cost? (a) ₹47 (b) ₹360 (c) ₹180 (d) ₹200
8. 8.₹336 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹28 (b) ₹168 (c) ₹196 (d) ₹140
9. 9.If 6 pens cost ₹30, how much do 2 pens cost? (a) ₹26 (b) ₹15 (c) ₹60 (d) ₹10
10. 10.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 17 days (c) 4 days (d) 6 days
11. 11.If 7 pens cost ₹77, how much do 11 pens cost? (a) ₹847 (b) ₹121 (c) ₹132 (d) ₹81
12. 12.₹196 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹14 (b) ₹126 (c) ₹98 (d) ₹70
13. 13.₹392 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹252 (b) ₹196 (c) ₹140 (d) ₹28
14. 14.If 5 pens cost ₹30, how much do 6 pens cost? (a) ₹180 (b) ₹42 (c) ₹36 (d) ₹31
15. 15.₹374 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹170 (b) ₹34 (c) ₹187 (d) ₹204
16. 16.5 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) 16 days (d) 15 days
17. 17.₹153 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹102 (b) ₹17 (c) ₹85 (d) ₹68
18. 18.₹25 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹10 (b) ₹5 (c) ₹20 (d) ₹15
19. 19.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 4 days (c) 7 days (d) 13 days
20. 20.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹56 (b) ₹63 (c) ₹7 (d) ₹35
21. 21.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 10 days (c) 19 days (d) 18 days
22. 22.If 7 notebooks cost ₹126, how much do 8 notebooks cost? (a) ₹162 (b) ₹144 (c) ₹127 (d) ₹1008
23. 23.If 6 mangoes cost ₹18, how much do 2 mangoes cost? (a) ₹6 (b) ₹36 (c) ₹9 (d) ₹14
24. 24.₹54 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹18 (b) ₹36 (c) ₹54 (d) ₹27
25. 25.If 7 mangoes cost ₹105, how much do 5 mangoes cost? (a) ₹90 (b) ₹75 (c) ₹103 (d) ₹525
26. 26.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 24 days (c) 23 days (d) 12 days
27. 27.₹210 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹210 (b) ₹35 (c) ₹175 (d) ₹105
28. 28.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 17 days (c) 12 days (d) 4 days
29. 29.If 8 mangoes cost ₹88, how much do 11 mangoes cost? (a) ₹91 (b) ₹132 (c) ₹968 (d) ₹121
30. 30.₹110 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹66 (b) ₹22 (c) ₹55 (d) ₹44
31. 31.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 25 days (d) 17 days
32. 32.If 3 pens cost ₹27, how much do 4 pens cost? (a) ₹28 (b) ₹45 (c) ₹108 (d) ₹36
33. 33.₹160 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹20 (b) ₹80 (c) ₹60 (d) ₹100
34. 34.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 1 day
35. 35.If 9 mangoes cost ₹90, how much do 4 mangoes cost? (a) ₹360 (b) ₹40 (c) ₹50 (d) ₹85
36. 36.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 22 days (c) 21 days (d) 13 days
37. 37.₹396 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹288 (b) ₹198 (c) ₹36 (d) ₹108
38. 38.₹261 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹116 (b) ₹174 (c) ₹29 (d) ₹145
39. 39.₹455 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹315 (b) ₹35 (c) ₹280 (d) ₹175
40. 40.₹374 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹68 (b) ₹306 (c) ₹187 (d) ₹34

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