Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 798 · 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 3 pens cost ₹54, how much do 9 pens cost? (a) ₹486 (b) ₹60 (c) ₹180 (d) ₹162
2. 2.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 40 days (b) 39 days (c) 17 days (d) 9 days
3. 3.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 13 days (b) 11 days (c) 16 days (d) 9 days
4. 4.6 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) 3 days (d) 13 days
5. 5.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 40 days (c) 39 days (d) 7 days
6. 6.If 3 notebooks cost ₹27, how much do 8 notebooks cost? (a) ₹32 (b) ₹72 (c) ₹216 (d) ₹81
7. 7.If 2 mangoes cost ₹30, how much do 7 mangoes cost? (a) ₹35 (b) ₹105 (c) ₹210 (d) ₹120
8. 8.₹396 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹288 (b) ₹36 (c) ₹108 (d) ₹198
9. 9.₹230 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹69 (b) ₹161 (c) ₹23 (d) ₹115
10. 10.If 7 kites cost ₹112, how much do 11 kites cost? (a) ₹116 (b) ₹1232 (c) ₹192 (d) ₹176
11. 11.If 9 pens cost ₹99, how much do 8 pens cost? (a) ₹792 (b) ₹98 (c) ₹99 (d) ₹88
12. 12.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 19 days (c) 18 days (d) 11 days
13. 13.If 2 mangoes cost ₹16, how much do 8 mangoes cost? (a) ₹72 (b) ₹22 (c) ₹128 (d) ₹64
14. 14.If 3 kites cost ₹51, how much do 6 kites cost? (a) ₹306 (b) ₹54 (c) ₹119 (d) ₹102
15. 15.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 13 days (c) 6 days (d) 7 days
16. 16.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 11 days (c) 15 days (d) 16 days
17. 17.If 7 mangoes cost ₹49, how much do 11 mangoes cost? (a) ₹53 (b) ₹539 (c) ₹77 (d) ₹84
18. 18.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 23 days (c) 22 days (d) 9 days
19. 19.₹539 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹98 (b) ₹441 (c) ₹490 (d) ₹49
20. 20.If 6 mangoes cost ₹126, how much do 10 mangoes cost? (a) ₹1260 (b) ₹231 (c) ₹210 (d) ₹130
21. 21.3 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 7 days (d) 6 days
22. 22.If 6 pens cost ₹24, how much do 4 pens cost? (a) ₹16 (b) ₹20 (c) ₹96 (d) ₹22
23. 23.₹456 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹266 (b) ₹228 (c) ₹38 (d) ₹190
24. 24.7 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) 6 days (d) 7 days
25. 25.If 3 notebooks cost ₹39, how much do 9 notebooks cost? (a) ₹130 (b) ₹117 (c) ₹351 (d) ₹45
26. 26.If 7 mangoes cost ₹105, how much do 3 mangoes cost? (a) ₹45 (b) ₹60 (c) ₹315 (d) ₹101
27. 27.If 7 pens cost ₹126, how much do 8 pens cost? (a) ₹144 (b) ₹162 (c) ₹1008 (d) ₹127
28. 28.6 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 30 days (b) 14 days (c) 31 days (d) 6 days
29. 29.₹468 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹234 (b) ₹195 (c) ₹39 (d) ₹273
30. 30.₹473 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹387 (b) ₹86 (c) ₹43 (d) ₹430
31. 31.If 6 pens cost ₹30, how much do 7 pens cost? (a) ₹40 (b) ₹210 (c) ₹35 (d) ₹31
32. 32.₹407 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹296 (b) ₹148 (c) ₹37 (d) ₹259
33. 33.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 8 days (d) 9 days
34. 34.₹49 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹14 (b) ₹42 (c) ₹35 (d) ₹7
35. 35.₹588 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹294 (b) ₹378 (c) ₹210 (d) ₹42
36. 36.If 4 mangoes cost ₹44, how much do 5 mangoes cost? (a) ₹55 (b) ₹220 (c) ₹45 (d) ₹66
37. 37.If 2 notebooks cost ₹42, how much do 11 notebooks cost? (a) ₹462 (b) ₹252 (c) ₹231 (d) ₹51
38. 38.₹418 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹228 (b) ₹209 (c) ₹190 (d) ₹38
39. 39.If 5 notebooks cost ₹25, how much do 6 notebooks cost? (a) ₹30 (b) ₹26 (c) ₹150 (d) ₹35
40. 40.If 2 kites cost ₹24, how much do 7 kites cost? (a) ₹29 (b) ₹84 (c) ₹96 (d) ₹168

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