Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 736 · 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.₹297 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹27 (b) ₹81 (c) ₹243 (d) ₹216
2. 2.₹72 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹56 (b) ₹8 (c) ₹36 (d) ₹16
3. 3.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 12 days (d) 16 days
4. 4.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 7 days (c) 6 days (d) 5 days
5. 5.₹154 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹22 (b) ₹77 (c) ₹110 (d) ₹44
6. 6.If 9 pens cost ₹144, how much do 2 pens cost? (a) ₹32 (b) ₹137 (c) ₹288 (d) ₹48
7. 7.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 3 days (c) 27 days (d) 17 days
8. 8.₹429 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹273 (b) ₹312 (c) ₹156 (d) ₹39
9. 9.₹231 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹21 (b) ₹189 (c) ₹210 (d) ₹42
10. 10.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 7 days (d) 4 days
11. 11.₹174 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹29 (b) ₹174 (c) ₹87 (d) ₹145
12. 12.₹336 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹192 (b) ₹48 (c) ₹144 (d) ₹168
13. 13.If 3 mangoes cost ₹36, how much do 9 mangoes cost? (a) ₹324 (b) ₹108 (c) ₹120 (d) ₹42
14. 14.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 4 days (d) 8 days
15. 15.If 2 pens cost ₹50, how much do 6 pens cost? (a) ₹175 (b) ₹300 (c) ₹150 (d) ₹54
16. 16.₹24 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹12 (b) ₹8 (c) ₹24 (d) ₹16
17. 17.₹65 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹65 (b) ₹52 (c) ₹13 (d) ₹53
18. 18.If 4 notebooks cost ₹32, how much do 12 notebooks cost? (a) ₹96 (b) ₹40 (c) ₹384 (d) ₹104
19. 19.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 19 days (c) 7 days (d) 40 days
20. 20.₹162 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹126 (b) ₹81 (c) ₹36 (d) ₹18
21. 21.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 6 days (d) 8 days
22. 22.₹341 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹155 (b) ₹186 (c) ₹31 (d) ₹217
23. 23.If 6 pens cost ₹114, how much do 3 pens cost? (a) ₹111 (b) ₹76 (c) ₹342 (d) ₹57
24. 24.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 17 days (c) 2 days (d) 4 days
25. 25.₹84 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹84 (b) ₹42 (c) ₹63 (d) ₹21
26. 26.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 3 days (c) 4 days (d) 15 days
27. 27.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 9 days (d) 10 days
28. 28.If 4 kites cost ₹68, how much do 9 kites cost? (a) ₹612 (b) ₹170 (c) ₹73 (d) ₹153
29. 29.₹429 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹132 (b) ₹297 (c) ₹330 (d) ₹33
30. 30.₹154 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹84 (b) ₹77 (c) ₹70 (d) ₹14
31. 31.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 5 days (d) 20 days
32. 32.₹108 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹96 (b) ₹54 (c) ₹12 (d) ₹108
33. 33.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 7 days (d) 12 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) 16 days (b) 15 days (c) 7 days (d) 11 days
35. 35.If 5 mangoes cost ₹95, how much do 10 mangoes cost? (a) ₹950 (b) ₹190 (c) ₹100 (d) ₹209
36. 36.₹221 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹153 (b) ₹170 (c) ₹68 (d) ₹17
37. 37.If 8 notebooks cost ₹24, how much do 5 notebooks cost? (a) ₹15 (b) ₹18 (c) ₹21 (d) ₹120
38. 38.₹45 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹36 (b) ₹9 (c) ₹18 (d) ₹27
39. 39.₹400 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹200 (b) ₹50 (c) ₹250 (d) ₹150
40. 40.₹140 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹70 (b) ₹50 (c) ₹10 (d) ₹90

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