Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 189 · 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. 1.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 13 days
2. 2.₹216 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹24 (b) ₹108 (c) ₹120 (d) ₹96
3. 3.₹440 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹220 (b) ₹44 (c) ₹440 (d) ₹396
4. 4.If 9 kites cost ₹153, how much do 12 kites cost? (a) ₹221 (b) ₹1836 (c) ₹204 (d) ₹156
5. 5.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 4 days (d) 7 days
6. 6.₹169 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹13 (b) ₹130 (c) ₹52 (d) ₹117
7. 7.₹96 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹56 (b) ₹48 (c) ₹40 (d) ₹8
8. 8.If 3 kites cost ₹24, how much do 9 kites cost? (a) ₹216 (b) ₹80 (c) ₹30 (d) ₹72
9. 9.₹392 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹245 (b) ₹196 (c) ₹49 (d) ₹147
10. 10.6 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 10 days (d) 4 days
11. 11.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 64 days (c) 7 days (d) 63 days
12. 12.₹253 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹115 (b) ₹23 (c) ₹161 (d) ₹138
13. 13.If 8 pens cost ₹24, how much do 10 pens cost? (a) ₹26 (b) ₹240 (c) ₹30 (d) ₹33
14. 14.If 8 mangoes cost ₹200, how much do 5 mangoes cost? (a) ₹125 (b) ₹1000 (c) ₹150 (d) ₹197
15. 15.₹45 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹5 (b) ₹40 (c) ₹10 (d) ₹35
16. 16.₹170 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹34 (b) ₹85 (c) ₹102 (d) ₹68
17. 17.If 9 kites cost ₹99, how much do 10 kites cost? (a) ₹121 (b) ₹100 (c) ₹110 (d) ₹990
18. 18.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 36 days (d) 18 days
19. 19.₹168 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹84 (b) ₹168 (c) ₹126 (d) ₹42
20. 20.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 7 days (d) 6 days
21. 21.If 8 pens cost ₹112, how much do 3 pens cost? (a) ₹107 (b) ₹56 (c) ₹42 (d) ₹336
22. 22.₹539 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹294 (b) ₹343 (c) ₹49 (d) ₹245
23. 23.₹32 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹32 (b) ₹24 (c) ₹16 (d) ₹8
24. 24.If 5 mangoes cost ₹85, how much do 7 mangoes cost? (a) ₹119 (b) ₹595 (c) ₹136 (d) ₹87
25. 25.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 30 days (b) 31 days (c) 17 days (d) 13 days
26. 26.4 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
27. 27.₹329 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹47 (b) ₹329 (c) ₹283 (d) ₹282
28. 28.₹220 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹110 (b) ₹66 (c) ₹154 (d) ₹22
29. 29.If 8 pens cost ₹152, how much do 4 pens cost? (a) ₹76 (b) ₹95 (c) ₹148 (d) ₹608
30. 30.If 3 pens cost ₹30, how much do 9 pens cost? (a) ₹36 (b) ₹100 (c) ₹270 (d) ₹90
31. 31.If 8 mangoes cost ₹88, how much do 4 mangoes cost? (a) ₹55 (b) ₹44 (c) ₹352 (d) ₹84
32. 32.If 3 pens cost ₹33, how much do 4 pens cost? (a) ₹34 (b) ₹44 (c) ₹132 (d) ₹55
33. 33.4 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 23 days (b) 7 days (c) 5 days (d) 45 days
34. 34.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 6 days (c) 8 days (d) 7 days
35. 35.If 2 pens cost ₹18, how much do 7 pens cost? (a) ₹23 (b) ₹72 (c) ₹63 (d) ₹126
36. 36.₹170 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹170 (b) ₹85 (c) ₹34 (d) ₹136
37. 37.If 7 kites cost ₹84, how much do 8 kites cost? (a) ₹108 (b) ₹85 (c) ₹672 (d) ₹96
38. 38.₹54 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹27 (b) ₹24 (c) ₹30 (d) ₹6
39. 39.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 12 days (b) 1 day (c) 3 days (d) 11 days
40. 40.If 8 mangoes cost ₹64, how much do 11 mangoes cost? (a) ₹67 (b) ₹88 (c) ₹96 (d) ₹704

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