Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 628 · 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.₹484 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹44 (b) ₹242 (c) ₹308 (d) ₹176
2. 2.If 2 notebooks cost ₹28, how much do 8 notebooks cost? (a) ₹224 (b) ₹126 (c) ₹34 (d) ₹112
3. 3.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 9 days (d) 8 days
4. 4.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 27 days (d) 13 days
5. 5.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 8 days (d) 18 days
6. 6.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 10 days (c) 11 days (d) 7 days
7. 7.If 2 pens cost ₹6, how much do 3 pens cost? (a) ₹9 (b) ₹18 (c) ₹7 (d) ₹12
8. 8.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 25 days (d) 13 days
9. 9.₹204 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹204 (b) ₹34 (c) ₹170 (d) ₹102
10. 10.If 5 pens cost ₹50, how much do 2 pens cost? (a) ₹100 (b) ₹20 (c) ₹30 (d) ₹47
11. 11.If 3 kites cost ₹75, how much do 8 kites cost? (a) ₹200 (b) ₹80 (c) ₹600 (d) ₹225
12. 12.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 6 days (d) 7 days
13. 13.₹198 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹18 (b) ₹126 (c) ₹99 (d) ₹72
14. 14.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 15 days (c) 21 days (d) 13 days
15. 15.If 9 pens cost ₹144, how much do 4 pens cost? (a) ₹80 (b) ₹576 (c) ₹64 (d) ₹139
16. 16.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 3 days (c) 11 days (d) 7 days
17. 17.₹100 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹50 (b) ₹100 (c) ₹90 (d) ₹10
18. 18.If 7 mangoes cost ₹112, how much do 4 mangoes cost? (a) ₹64 (b) ₹80 (c) ₹109 (d) ₹448
19. 19.₹45 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹30 (b) ₹31 (c) ₹15 (d) ₹45
20. 20.₹261 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹261 (b) ₹232 (c) ₹29 (d) ₹233
21. 21.₹187 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹85 (b) ₹17 (c) ₹102 (d) ₹119
22. 22.9 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 7 days (d) 16 days
23. 23.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 29 days (b) 13 days (c) 28 days (d) 3 days
24. 24.If 6 notebooks cost ₹30, how much do 5 notebooks cost? (a) ₹150 (b) ₹30 (c) ₹25 (d) ₹29
25. 25.If 3 kites cost ₹36, how much do 2 kites cost? (a) ₹24 (b) ₹36 (c) ₹35 (d) ₹72
26. 26.If 4 mangoes cost ₹12, how much do 3 mangoes cost? (a) ₹11 (b) ₹36 (c) ₹12 (d) ₹9
27. 27.If 3 notebooks cost ₹69, how much do 5 notebooks cost? (a) ₹345 (b) ₹138 (c) ₹115 (d) ₹71
28. 28.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 23 days (b) 22 days (c) 15 days (d) 7 days
29. 29.8 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 14 days (d) 9 days
30. 30.If 7 pens cost ₹175, how much do 5 pens cost? (a) ₹173 (b) ₹875 (c) ₹150 (d) ₹125
31. 31.If 2 kites cost ₹18, how much do 3 kites cost? (a) ₹54 (b) ₹27 (c) ₹19 (d) ₹36
32. 32.If 7 notebooks cost ₹154, how much do 8 notebooks cost? (a) ₹155 (b) ₹176 (c) ₹198 (d) ₹1232
33. 33.If 9 notebooks cost ₹135, how much do 5 notebooks cost? (a) ₹75 (b) ₹131 (c) ₹90 (d) ₹675
34. 34.₹288 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹144 (b) ₹32 (c) ₹160 (d) ₹128
35. 35.If 9 pens cost ₹171, how much do 8 pens cost? (a) ₹170 (b) ₹171 (c) ₹152 (d) ₹1368
36. 36.₹105 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹21 (b) ₹84 (c) ₹42 (d) ₹63
37. 37.If 5 mangoes cost ₹80, how much do 6 mangoes cost? (a) ₹81 (b) ₹112 (c) ₹480 (d) ₹96
38. 38.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 5 days (d) 12 days
39. 39.₹473 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹258 (b) ₹301 (c) ₹43 (d) ₹215
40. 40.If 6 pens cost ₹48, how much do 2 pens cost? (a) ₹44 (b) ₹96 (c) ₹16 (d) ₹24

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