Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 341 · 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 2 pens cost ₹48, how much do 3 pens cost? (a) ₹144 (b) ₹49 (c) ₹96 (d) ₹72
2. 2.₹330 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹99 (b) ₹33 (c) ₹165 (d) ₹231
3. 3.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 9 days (c) 2 days (d) 8 days
4. 4.If 4 notebooks cost ₹36, how much do 8 notebooks cost? (a) ₹72 (b) ₹288 (c) ₹40 (d) ₹81
5. 5.₹176 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹66 (b) ₹88 (c) ₹110 (d) ₹22
6. 6.₹432 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹384 (b) ₹48 (c) ₹432 (d) ₹216
7. 7.₹240 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹96 (b) ₹120 (c) ₹48 (d) ₹144
8. 8.₹156 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹65 (b) ₹78 (c) ₹13 (d) ₹91
9. 9.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 32 days (b) 33 days (c) 14 days (d) 2 days
10. 10.If 5 mangoes cost ₹45, how much do 4 mangoes cost? (a) ₹45 (b) ₹180 (c) ₹36 (d) ₹44
11. 11.₹418 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹209 (b) ₹304 (c) ₹38 (d) ₹114
12. 12.₹304 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹152 (b) ₹266 (c) ₹38 (d) ₹304
13. 13.₹168 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹84 (b) ₹21 (c) ₹168 (d) ₹147
14. 14.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 6 days (d) 4 days
15. 15.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 1 day (d) 11 days
16. 16.₹180 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹90 (b) ₹100 (c) ₹20 (d) ₹80
17. 17.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 18 days (c) 19 days (d) 7 days
18. 18.₹117 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹81 (b) ₹72 (c) ₹9 (d) ₹45
19. 19.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 2 days (c) 12 days (d) 19 days
20. 20.₹63 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹14 (b) ₹56 (c) ₹7 (d) ₹49
21. 21.4 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 20 days (c) 4 days (d) 36 days
22. 22.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 21 days (b) 17 days (c) 13 days (d) 22 days
23. 23.₹444 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹259 (b) ₹37 (c) ₹185 (d) ₹222
24. 24.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 40 days (c) 19 days (d) 7 days
25. 25.₹364 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹182 (b) ₹140 (c) ₹28 (d) ₹224
26. 26.₹450 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹450 (b) ₹50 (c) ₹225 (d) ₹400
27. 27.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 16 days (c) 10 days (d) 17 days
28. 28.₹637 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹49 (b) ₹441 (c) ₹392 (d) ₹245
29. 29.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 20 days (b) 5 days (c) 13 days (d) 7 days
30. 30.₹195 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹75 (b) ₹120 (c) ₹135 (d) ₹15
31. 31.If 5 kites cost ₹45, how much do 4 kites cost? (a) ₹45 (b) ₹44 (c) ₹180 (d) ₹36
32. 32.₹57 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹19 (b) ₹38 (c) ₹57 (d) ₹39
33. 33.₹36 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹12 (b) ₹24 (c) ₹18 (d) ₹36
34. 34.If 2 pens cost ₹42, how much do 3 pens cost? (a) ₹63 (b) ₹126 (c) ₹43 (d) ₹84
35. 35.If 7 pens cost ₹112, how much do 8 pens cost? (a) ₹113 (b) ₹128 (c) ₹144 (d) ₹896
36. 36.If 8 pens cost ₹24, how much do 12 pens cost? (a) ₹39 (b) ₹36 (c) ₹288 (d) ₹28
37. 37.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 2 days (c) 11 days (d) 8 days
38. 38.₹200 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹20 (b) ₹100 (c) ₹200 (d) ₹180
39. 39.₹290 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹29 (b) ₹145 (c) ₹261 (d) ₹290
40. 40.If 6 mangoes cost ₹72, how much do 7 mangoes cost? (a) ₹504 (b) ₹73 (c) ₹84 (d) ₹96

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