Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 809 · 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.₹700 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹350 (b) ₹250 (c) ₹50 (d) ₹450
2. 2.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 34 days (c) 7 days (d) 33 days
3. 3.₹54 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹12 (b) ₹6 (c) ₹42 (d) ₹27
4. 4.₹195 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹135 (b) ₹75 (c) ₹15 (d) ₹120
5. 5.If 7 pens cost ₹77, how much do 5 pens cost? (a) ₹55 (b) ₹385 (c) ₹66 (d) ₹75
6. 6.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 4 days (d) 27 days
7. 7.₹77 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹42 (b) ₹49 (c) ₹7 (d) ₹35
8. 8.If 5 notebooks cost ₹20, how much do 10 notebooks cost? (a) ₹44 (b) ₹40 (c) ₹25 (d) ₹200
9. 9.If 4 kites cost ₹84, how much do 9 kites cost? (a) ₹89 (b) ₹210 (c) ₹756 (d) ₹189
10. 10.8 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 14 days (d) 16 days
11. 11.If 4 kites cost ₹92, how much do 5 kites cost? (a) ₹115 (b) ₹460 (c) ₹138 (d) ₹93
12. 12.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 35 days (b) 5 days (c) 15 days (d) 36 days
13. 13.₹348 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹203 (b) ₹174 (c) ₹145 (d) ₹29
14. 14.If 9 kites cost ₹54, how much do 3 kites cost? (a) ₹18 (b) ₹48 (c) ₹162 (d) ₹24
15. 15.If 5 kites cost ₹125, how much do 11 kites cost? (a) ₹300 (b) ₹131 (c) ₹275 (d) ₹1375
16. 16.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 19 days (b) 27 days (c) 28 days (d) 11 days
17. 17.₹368 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹184 (b) ₹138 (c) ₹46 (d) ₹230
18. 18.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 4 days (d) 2 days
19. 19.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 17 days (d) 4 days
20. 20.If 4 mangoes cost ₹88, how much do 6 mangoes cost? (a) ₹132 (b) ₹154 (c) ₹90 (d) ₹528
21. 21.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 23 days (d) 22 days
22. 22.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 5 days (d) 9 days
23. 23.If 3 notebooks cost ₹54, how much do 2 notebooks cost? (a) ₹53 (b) ₹36 (c) ₹54 (d) ₹108
24. 24.5 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 20 days (c) 21 days (d) 10 days
25. 25.₹81 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹27 (b) ₹81 (c) ₹54 (d) ₹55
26. 26.If 6 mangoes cost ₹102, how much do 4 mangoes cost? (a) ₹100 (b) ₹68 (c) ₹408 (d) ₹85
27. 27.If 3 mangoes cost ₹48, how much do 9 mangoes cost? (a) ₹432 (b) ₹54 (c) ₹144 (d) ₹160
28. 28.If 9 mangoes cost ₹36, how much do 2 mangoes cost? (a) ₹72 (b) ₹29 (c) ₹8 (d) ₹12
29. 29.₹210 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹168 (b) ₹42 (c) ₹105 (d) ₹210
30. 30.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 40 days (d) 39 days
31. 31.If 6 kites cost ₹150, how much do 4 kites cost? (a) ₹148 (b) ₹100 (c) ₹125 (d) ₹600
32. 32.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 15 days (b) 16 days (c) 13 days (d) 17 days
33. 33.If 9 kites cost ₹198, how much do 3 kites cost? (a) ₹66 (b) ₹594 (c) ₹192 (d) ₹88
34. 34.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 15 days (d) 20 days
35. 35.If 4 mangoes cost ₹60, how much do 10 mangoes cost? (a) ₹165 (b) ₹66 (c) ₹600 (d) ₹150
36. 36.₹429 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹165 (b) ₹297 (c) ₹264 (d) ₹33
37. 37.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 12 days (d) 7 days
38. 38.If 9 notebooks cost ₹180, how much do 10 notebooks cost? (a) ₹181 (b) ₹200 (c) ₹1800 (d) ₹220
39. 39.If 7 kites cost ₹28, how much do 8 kites cost? (a) ₹36 (b) ₹29 (c) ₹32 (d) ₹224
40. 40.₹330 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹99 (b) ₹231 (c) ₹33 (d) ₹165

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