Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 871 · 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 7 mangoes cost ₹140, how much do 10 mangoes cost? (a) ₹143 (b) ₹220 (c) ₹200 (d) ₹1400
2. 2.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 7 days (d) 14 days
3. 3.5 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 30 days (c) 31 days (d) 9 days
4. 4.₹64 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹16 (b) ₹32 (c) ₹64 (d) ₹48
5. 5.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 9 days (d) 1 day
6. 6.8 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 60 days (d) 61 days
7. 7.If 6 mangoes cost ₹72, how much do 10 mangoes cost? (a) ₹120 (b) ₹132 (c) ₹76 (d) ₹720
8. 8.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 37 days (c) 3 days (d) 36 days
9. 9.₹288 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹160 (b) ₹32 (c) ₹144 (d) ₹128
10. 10.₹252 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹216 (b) ₹252 (c) ₹36 (d) ₹126
11. 11.If 8 mangoes cost ₹40, how much do 9 mangoes cost? (a) ₹360 (b) ₹45 (c) ₹41 (d) ₹50
12. 12.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 27 days (c) 15 days (d) 28 days
13. 13.If 2 pens cost ₹22, how much do 4 pens cost? (a) ₹88 (b) ₹24 (c) ₹44 (d) ₹55
14. 14.₹171 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹19 (b) ₹38 (c) ₹152 (d) ₹133
15. 15.If 9 notebooks cost ₹72, how much do 2 notebooks cost? (a) ₹16 (b) ₹144 (c) ₹24 (d) ₹65
16. 16.If 5 kites cost ₹55, how much do 6 kites cost? (a) ₹56 (b) ₹330 (c) ₹66 (d) ₹77
17. 17.If 4 kites cost ₹52, how much do 5 kites cost? (a) ₹260 (b) ₹53 (c) ₹65 (d) ₹78
18. 18.₹90 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹9 (b) ₹27 (c) ₹63 (d) ₹45
19. 19.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 16 days (c) 9 days (d) 15 days
20. 20.6 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 19 days (b) 9 days (c) 11 days (d) 25 days
21. 21.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 33 days (b) 32 days (c) 2 days (d) 14 days
22. 22.₹520 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹360 (b) ₹160 (c) ₹260 (d) ₹40
23. 23.If 5 kites cost ₹25, how much do 10 kites cost? (a) ₹50 (b) ₹30 (c) ₹55 (d) ₹250
24. 24.₹96 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹48 (b) ₹96 (c) ₹72 (d) ₹24
25. 25.If 6 kites cost ₹150, how much do 2 kites cost? (a) ₹50 (b) ₹75 (c) ₹300 (d) ₹146
26. 26.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 12 days (c) 18 days (d) 2 days
27. 27.If 6 notebooks cost ₹102, how much do 7 notebooks cost? (a) ₹136 (b) ₹103 (c) ₹714 (d) ₹119
28. 28.8 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 13 days (c) 17 days (d) 16 days
29. 29.₹363 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹264 (b) ₹132 (c) ₹33 (d) ₹231
30. 30.If 8 mangoes cost ₹80, how much do 4 mangoes cost? (a) ₹76 (b) ₹50 (c) ₹40 (d) ₹320
31. 31.If 3 mangoes cost ₹9, how much do 2 mangoes cost? (a) ₹8 (b) ₹6 (c) ₹18 (d) ₹9
32. 32.If 8 notebooks cost ₹48, how much do 2 notebooks cost? (a) ₹96 (b) ₹12 (c) ₹18 (d) ₹42
33. 33.₹264 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹24 (b) ₹132 (c) ₹120 (d) ₹144
34. 34.₹442 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹136 (b) ₹221 (c) ₹34 (d) ₹306
35. 35.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 25 days (b) 9 days (c) 13 days (d) 17 days
36. 36.If 3 notebooks cost ₹36, how much do 8 notebooks cost? (a) ₹96 (b) ₹288 (c) ₹41 (d) ₹108
37. 37.₹495 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹45 (b) ₹225 (c) ₹270 (d) ₹315
38. 38.If 2 kites cost ₹18, how much do 7 kites cost? (a) ₹63 (b) ₹23 (c) ₹72 (d) ₹126
39. 39.₹153 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹17 (b) ₹119 (c) ₹136 (d) ₹34
40. 40.If 4 mangoes cost ₹84, how much do 6 mangoes cost? (a) ₹504 (b) ₹86 (c) ₹126 (d) ₹147

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