Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 977 · 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 6 pens cost ₹48, how much do 9 pens cost? (a) ₹72 (b) ₹51 (c) ₹80 (d) ₹432
2. 2.If 6 notebooks cost ₹126, how much do 2 notebooks cost? (a) ₹63 (b) ₹252 (c) ₹42 (d) ₹122
3. 3.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 31 days (d) 30 days
4. 4.If 7 pens cost ₹42, how much do 9 pens cost? (a) ₹44 (b) ₹54 (c) ₹378 (d) ₹60
5. 5.₹350 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹125 (b) ₹25 (c) ₹225 (d) ₹175
6. 6.If 8 mangoes cost ₹96, how much do 2 mangoes cost? (a) ₹90 (b) ₹24 (c) ₹192 (d) ₹36
7. 7.If 4 kites cost ₹68, how much do 10 kites cost? (a) ₹187 (b) ₹74 (c) ₹680 (d) ₹170
8. 8.₹136 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹51 (b) ₹17 (c) ₹85 (d) ₹68
9. 9.If 3 mangoes cost ₹72, how much do 4 mangoes cost? (a) ₹120 (b) ₹288 (c) ₹73 (d) ₹96
10. 10.₹630 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹45 (b) ₹225 (c) ₹315 (d) ₹405
11. 11.If 6 pens cost ₹36, how much do 7 pens cost? (a) ₹42 (b) ₹252 (c) ₹37 (d) ₹48
12. 12.9 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 11 days (d) 9 days
13. 13.If 3 notebooks cost ₹15, how much do 11 notebooks cost? (a) ₹55 (b) ₹165 (c) ₹23 (d) ₹60
14. 14.₹50 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹10 (b) ₹25 (c) ₹40 (d) ₹50
15. 15.If 7 notebooks cost ₹56, how much do 4 notebooks cost? (a) ₹224 (b) ₹32 (c) ₹53 (d) ₹40
16. 16.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 21 days (c) 22 days (d) 13 days
17. 17.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 4 days (d) 7 days
18. 18.If 9 pens cost ₹207, how much do 11 pens cost? (a) ₹2277 (b) ₹276 (c) ₹209 (d) ₹253
19. 19.₹476 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹34 (b) ₹306 (c) ₹238 (d) ₹170
20. 20.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 16 days (d) 9 days
21. 21.₹252 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹224 (b) ₹28 (c) ₹126 (d) ₹252
22. 22.If 5 pens cost ₹125, how much do 8 pens cost? (a) ₹128 (b) ₹225 (c) ₹200 (d) ₹1000
23. 23.6 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 21 days (b) 12 days (c) 16 days (d) 22 days
24. 24.If 6 mangoes cost ₹30, how much do 8 mangoes cost? (a) ₹32 (b) ₹240 (c) ₹45 (d) ₹40
25. 25.₹455 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹175 (b) ₹280 (c) ₹315 (d) ₹35
26. 26.₹492 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹246 (b) ₹205 (c) ₹41 (d) ₹287
27. 27.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 6 days (d) 8 days
28. 28.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 28 days (b) 17 days (c) 7 days (d) 11 days
29. 29.₹209 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹19 (b) ₹114 (c) ₹95 (d) ₹133
30. 30.If 5 mangoes cost ₹15, how much do 11 mangoes cost? (a) ₹21 (b) ₹165 (c) ₹33 (d) ₹36
31. 31.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 21 days (c) 22 days (d) 13 days
32. 32.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 18 days (c) 10 days (d) 6 days
33. 33.₹64 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹40 (b) ₹32 (c) ₹8 (d) ₹24
34. 34.If 3 pens cost ₹24, how much do 7 pens cost? (a) ₹168 (b) ₹64 (c) ₹56 (d) ₹28
35. 35.If 4 notebooks cost ₹88, how much do 12 notebooks cost? (a) ₹1056 (b) ₹286 (c) ₹96 (d) ₹264
36. 36.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 12 days (d) 4 days
37. 37.₹564 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹235 (b) ₹329 (c) ₹47 (d) ₹282
38. 38.9 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 18 days (c) 9 days (d) 15 days
39. 39.₹60 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹5 (b) ₹25 (c) ₹35 (d) ₹30
40. 40.If 3 mangoes cost ₹39, how much do 11 mangoes cost? (a) ₹143 (b) ₹47 (c) ₹156 (d) ₹429

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