Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 795 · 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. 1.4 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 14 days (d) 13 days
2. 2.If 9 notebooks cost ₹207, how much do 5 notebooks cost? (a) ₹115 (b) ₹203 (c) ₹138 (d) ₹1035
3. 3.If 7 notebooks cost ₹21, how much do 5 notebooks cost? (a) ₹18 (b) ₹15 (c) ₹105 (d) ₹19
4. 4.If 3 mangoes cost ₹63, how much do 6 mangoes cost? (a) ₹126 (b) ₹378 (c) ₹66 (d) ₹147
5. 5.₹392 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹140 (b) ₹252 (c) ₹196 (d) ₹28
6. 6.If 4 pens cost ₹80, how much do 8 pens cost? (a) ₹160 (b) ₹84 (c) ₹180 (d) ₹640
7. 7.If 3 mangoes cost ₹12, how much do 12 mangoes cost? (a) ₹144 (b) ₹52 (c) ₹48 (d) ₹21
8. 8.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 11 days (c) 18 days (d) 13 days
9. 9.If 6 kites cost ₹30, how much do 3 kites cost? (a) ₹27 (b) ₹90 (c) ₹15 (d) ₹20
10. 10.If 6 pens cost ₹114, how much do 3 pens cost? (a) ₹76 (b) ₹342 (c) ₹111 (d) ₹57
11. 11.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 45 days (c) 11 days (d) 5 days
12. 12.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 17 days (d) 4 days
13. 13.If 7 kites cost ₹77, how much do 8 kites cost? (a) ₹88 (b) ₹78 (c) ₹99 (d) ₹616
14. 14.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 10 days (d) 11 days
15. 15.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 5 days (c) 6 days (d) 4 days
16. 16.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 11 days (c) 21 days (d) 1 day
17. 17.₹450 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹315 (b) ₹45 (c) ₹225 (d) ₹135
18. 18.₹155 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹31 (b) ₹125 (c) ₹124 (d) ₹155
19. 19.₹481 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹296 (b) ₹37 (c) ₹333 (d) ₹185
20. 20.If 9 pens cost ₹27, how much do 7 pens cost? (a) ₹24 (b) ₹21 (c) ₹25 (d) ₹189
21. 21.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 8 days (d) 2 days
22. 22.₹192 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹16 (b) ₹112 (c) ₹96 (d) ₹80
23. 23.₹280 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹28 (b) ₹140 (c) ₹252 (d) ₹280
24. 24.If 9 kites cost ₹45, how much do 10 kites cost? (a) ₹55 (b) ₹50 (c) ₹46 (d) ₹450
25. 25.If 2 kites cost ₹30, how much do 3 kites cost? (a) ₹60 (b) ₹90 (c) ₹31 (d) ₹45
26. 26.If 8 notebooks cost ₹176, how much do 5 notebooks cost? (a) ₹173 (b) ₹880 (c) ₹110 (d) ₹132
27. 27.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 13 days (d) 3 days
28. 28.If 2 mangoes cost ₹46, how much do 7 mangoes cost? (a) ₹322 (b) ₹51 (c) ₹184 (d) ₹161
29. 29.₹221 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹170 (b) ₹17 (c) ₹68 (d) ₹153
30. 30.₹117 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹81 (b) ₹9 (c) ₹45 (d) ₹72
31. 31.₹520 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹320 (b) ₹260 (c) ₹40 (d) ₹200
32. 32.If 3 kites cost ₹63, how much do 2 kites cost? (a) ₹63 (b) ₹62 (c) ₹42 (d) ₹126
33. 33.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 9 days (d) 3 days
34. 34.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 8 days (d) 3 days
35. 35.If 8 pens cost ₹64, how much do 7 pens cost? (a) ₹448 (b) ₹56 (c) ₹64 (d) ₹63
36. 36.If 4 mangoes cost ₹72, how much do 10 mangoes cost? (a) ₹78 (b) ₹180 (c) ₹198 (d) ₹720
37. 37.If 6 mangoes cost ₹120, how much do 3 mangoes cost? (a) ₹80 (b) ₹117 (c) ₹60 (d) ₹360
38. 38.If 3 pens cost ₹42, how much do 10 pens cost? (a) ₹49 (b) ₹140 (c) ₹420 (d) ₹154
39. 39.If 7 pens cost ₹49, how much do 5 pens cost? (a) ₹47 (b) ₹245 (c) ₹35 (d) ₹42
40. 40.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 4 days (d) 2 days

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