Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 396 · 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.₹598 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹414 (b) ₹299 (c) ₹46 (d) ₹184
2. 2.If 7 kites cost ₹84, how much do 11 kites cost? (a) ₹144 (b) ₹924 (c) ₹132 (d) ₹88
3. 3.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 22 days (d) 23 days
4. 4.If 3 notebooks cost ₹54, how much do 8 notebooks cost? (a) ₹162 (b) ₹59 (c) ₹432 (d) ₹144
5. 5.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 2 days (d) 4 days
6. 6.If 6 mangoes cost ₹24, how much do 8 mangoes cost? (a) ₹36 (b) ₹26 (c) ₹192 (d) ₹32
7. 7.If 6 kites cost ₹120, how much do 2 kites cost? (a) ₹40 (b) ₹60 (c) ₹116 (d) ₹240
8. 8.₹115 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹93 (b) ₹23 (c) ₹115 (d) ₹92
9. 9.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 8 days (c) 9 days (d) 7 days
10. 10.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 28 days (b) 7 days (c) 10 days (d) 18 days
11. 11.₹231 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹33 (b) ₹132 (c) ₹165 (d) ₹99
12. 12.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 6 days (d) 7 days
13. 13.If 4 notebooks cost ₹36, how much do 11 notebooks cost? (a) ₹396 (b) ₹99 (c) ₹43 (d) ₹108
14. 14.₹155 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹31 (b) ₹124 (c) ₹93 (d) ₹62
15. 15.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 19 days (c) 4 days (d) 49 days
16. 16.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 9 days (d) 10 days
17. 17.If 4 pens cost ₹72, how much do 8 pens cost? (a) ₹576 (b) ₹144 (c) ₹76 (d) ₹162
18. 18.4 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 6 days (d) 5 days
19. 19.If 4 pens cost ₹96, how much do 8 pens cost? (a) ₹768 (b) ₹216 (c) ₹100 (d) ₹192
20. 20.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 3 days (d) 16 days
21. 21.If 2 kites cost ₹12, how much do 8 kites cost? (a) ₹48 (b) ₹18 (c) ₹54 (d) ₹96
22. 22.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 22 days (c) 9 days (d) 13 days
23. 23.If 2 notebooks cost ₹30, how much do 10 notebooks cost? (a) ₹38 (b) ₹150 (c) ₹300 (d) ₹165
24. 24.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 12 days (c) 2 days (d) 3 days
25. 25.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 12 days (b) 2 days (c) 10 days (d) 3 days
26. 26.₹75 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹51 (b) ₹75 (c) ₹50 (d) ₹25
27. 27.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 17 days (c) 13 days (d) 11 days
28. 28.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 3 days (d) 2 days
29. 29.₹261 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹29 (b) ₹261 (c) ₹232 (d) ₹233
30. 30.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 26 days (c) 13 days (d) 28 days
31. 31.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 13 days (d) 17 days
32. 32.If 4 notebooks cost ₹20, how much do 11 notebooks cost? (a) ₹27 (b) ₹60 (c) ₹220 (d) ₹55
33. 33.5 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) 6 days (d) 5 days
34. 34.₹390 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹351 (b) ₹39 (c) ₹195 (d) ₹390
35. 35.If 2 kites cost ₹20, how much do 3 kites cost? (a) ₹40 (b) ₹21 (c) ₹30 (d) ₹60
36. 36.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 28 days (c) 29 days (d) 13 days
37. 37.If 2 kites cost ₹50, how much do 9 kites cost? (a) ₹250 (b) ₹450 (c) ₹225 (d) ₹57
38. 38.If 9 mangoes cost ₹63, how much do 5 mangoes cost? (a) ₹59 (b) ₹42 (c) ₹315 (d) ₹35
39. 39.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 3 days (d) 10 days
40. 40.₹198 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹18 (b) ₹72 (c) ₹126 (d) ₹99

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