Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 279 · 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 8 pens cost ₹128, how much do 7 pens cost? (a) ₹896 (b) ₹112 (c) ₹127 (d) ₹128
2. 2.If 9 kites cost ₹135, how much do 10 kites cost? (a) ₹165 (b) ₹136 (c) ₹1350 (d) ₹150
3. 3.If 3 kites cost ₹54, how much do 6 kites cost? (a) ₹126 (b) ₹108 (c) ₹324 (d) ₹57
4. 4.If 6 kites cost ₹150, how much do 9 kites cost? (a) ₹250 (b) ₹225 (c) ₹153 (d) ₹1350
5. 5.₹550 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹350 (b) ₹200 (c) ₹275 (d) ₹50
6. 6.₹56 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹21 (b) ₹28 (c) ₹7 (d) ₹35
7. 7.₹611 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹47 (b) ₹235 (c) ₹423 (d) ₹376
8. 8.8 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 10 days (d) 7 days
9. 9.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 10 days (c) 17 days (d) 16 days
10. 10.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 57 days (c) 8 days (d) 56 days
11. 11.If 6 mangoes cost ₹84, how much do 11 mangoes cost? (a) ₹154 (b) ₹924 (c) ₹168 (d) ₹89
12. 12.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 45 days (c) 21 days (d) 9 days
13. 13.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 13 days (b) 4 days (c) 6 days (d) 5 days
14. 14.If 9 pens cost ₹36, how much do 10 pens cost? (a) ₹40 (b) ₹360 (c) ₹44 (d) ₹37
15. 15.₹363 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹33 (b) ₹231 (c) ₹198 (d) ₹165
16. 16.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 20 days (c) 15 days (d) 5 days
17. 17.If 7 mangoes cost ₹84, how much do 5 mangoes cost? (a) ₹60 (b) ₹420 (c) ₹82 (d) ₹72
18. 18.If 2 notebooks cost ₹10, how much do 5 notebooks cost? (a) ₹25 (b) ₹13 (c) ₹30 (d) ₹50
19. 19.If 7 pens cost ₹126, how much do 3 pens cost? (a) ₹122 (b) ₹54 (c) ₹378 (d) ₹72
20. 20.₹252 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹28 (b) ₹112 (c) ₹140 (d) ₹126
21. 21.₹110 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹55 (b) ₹33 (c) ₹11 (d) ₹77
22. 22.If 5 kites cost ₹50, how much do 3 kites cost? (a) ₹30 (b) ₹40 (c) ₹48 (d) ₹150
23. 23.₹72 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹8 (b) ₹36 (c) ₹72 (d) ₹64
24. 24.4 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 14 days (c) 10 days (d) 18 days
25. 25.₹130 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹10 (b) ₹65 (c) ₹50 (d) ₹80
26. 26.If 4 kites cost ₹60, how much do 9 kites cost? (a) ₹150 (b) ₹540 (c) ₹65 (d) ₹135
27. 27.₹20 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹10 (b) ₹15 (c) ₹20 (d) ₹5
28. 28.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 19 days (d) 2 days
29. 29.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 5 days (d) 7 days
30. 30.₹144 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹112 (b) ₹72 (c) ₹32 (d) ₹16
31. 31.₹161 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹23 (b) ₹69 (c) ₹92 (d) ₹115
32. 32.If 7 notebooks cost ₹28, how much do 6 notebooks cost? (a) ₹24 (b) ₹28 (c) ₹27 (d) ₹168
33. 33.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 5 days (d) 18 days
34. 34.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 7 days (d) 15 days
35. 35.If 4 notebooks cost ₹76, how much do 3 notebooks cost? (a) ₹57 (b) ₹76 (c) ₹75 (d) ₹228
36. 36.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 28 days (d) 27 days
37. 37.If 8 pens cost ₹64, how much do 9 pens cost? (a) ₹65 (b) ₹576 (c) ₹80 (d) ₹72
38. 38.If 4 pens cost ₹68, how much do 6 pens cost? (a) ₹102 (b) ₹408 (c) ₹119 (d) ₹70
39. 39.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 13 days (d) 25 days
40. 40.If 3 mangoes cost ₹72, how much do 4 mangoes cost? (a) ₹288 (b) ₹73 (c) ₹96 (d) ₹120

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