Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 962 · 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 ₹18, how much do 5 mangoes cost? (a) ₹90 (b) ₹21 (c) ₹54 (d) ₹45
2. 2.₹50 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹30 (b) ₹10 (c) ₹20 (d) ₹25
3. 3.If 6 mangoes cost ₹36, how much do 3 mangoes cost? (a) ₹108 (b) ₹33 (c) ₹18 (d) ₹24
4. 4.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 7 days (c) 40 days (d) 19 days
5. 5.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 19 days (c) 49 days (d) 4 days
6. 6.If 2 mangoes cost ₹48, how much do 12 mangoes cost? (a) ₹288 (b) ₹576 (c) ₹312 (d) ₹58
7. 7.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 5 days (c) 15 days (d) 35 days
8. 8.₹90 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹30 (b) ₹90 (c) ₹60 (d) ₹45
9. 9.₹225 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹225 (b) ₹201 (c) ₹200 (d) ₹25
10. 10.₹420 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹42 (b) ₹126 (c) ₹210 (d) ₹294
11. 11.If 3 mangoes cost ₹45, how much do 4 mangoes cost? (a) ₹60 (b) ₹75 (c) ₹46 (d) ₹180
12. 12.₹135 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹135 (b) ₹45 (c) ₹91 (d) ₹90
13. 13.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 8 days (d) 7 days
14. 14.₹410 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹205 (b) ₹41 (c) ₹287 (d) ₹123
15. 15.If 9 pens cost ₹198, how much do 4 pens cost? (a) ₹88 (b) ₹792 (c) ₹110 (d) ₹193
16. 16.If 7 mangoes cost ₹56, how much do 8 mangoes cost? (a) ₹57 (b) ₹64 (c) ₹72 (d) ₹448
17. 17.₹168 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹147 (b) ₹84 (c) ₹21 (d) ₹168
18. 18.If 7 mangoes cost ₹49, how much do 4 mangoes cost? (a) ₹196 (b) ₹35 (c) ₹46 (d) ₹28
19. 19.₹90 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹90 (b) ₹9 (c) ₹45 (d) ₹81
20. 20.₹80 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹16 (b) ₹80 (c) ₹64 (d) ₹40
21. 21.₹329 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹282 (b) ₹47 (c) ₹94 (d) ₹235
22. 22.6 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 10 days (c) 9 days (d) 14 days
23. 23.If 9 kites cost ₹153, how much do 7 kites cost? (a) ₹1071 (b) ₹119 (c) ₹136 (d) ₹151
24. 24.If 3 notebooks cost ₹66, how much do 4 notebooks cost? (a) ₹67 (b) ₹88 (c) ₹110 (d) ₹264
25. 25.If 2 notebooks cost ₹42, how much do 11 notebooks cost? (a) ₹252 (b) ₹462 (c) ₹51 (d) ₹231
26. 26.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 2 days (d) 3 days
27. 27.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 13 days (c) 26 days (d) 27 days
28. 28.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 13 days (c) 11 days (d) 10 days
29. 29.₹550 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹275 (b) ₹350 (c) ₹200 (d) ₹50
30. 30.₹230 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹92 (b) ₹46 (c) ₹138 (d) ₹115
31. 31.₹188 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹188 (b) ₹141 (c) ₹94 (d) ₹47
32. 32.If 3 pens cost ₹12, how much do 4 pens cost? (a) ₹48 (b) ₹20 (c) ₹13 (d) ₹16
33. 33.If 7 pens cost ₹168, how much do 8 pens cost? (a) ₹192 (b) ₹216 (c) ₹169 (d) ₹1344
34. 34.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹12 (b) ₹108 (c) ₹60 (d) ₹84
35. 35.If 6 pens cost ₹102, how much do 12 pens cost? (a) ₹204 (b) ₹108 (c) ₹1224 (d) ₹221
36. 36.If 8 pens cost ₹160, how much do 7 pens cost? (a) ₹159 (b) ₹1120 (c) ₹140 (d) ₹160
37. 37.If 2 pens cost ₹48, how much do 5 pens cost? (a) ₹51 (b) ₹120 (c) ₹240 (d) ₹144
38. 38.₹80 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹40 (b) ₹56 (c) ₹24 (d) ₹8
39. 39.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 22 days (c) 21 days (d) 1 day
40. 40.6 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 12 days (c) 13 days (d) 3 days

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