Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 546 · 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 2 kites cost ₹48, how much do 3 kites cost? (a) ₹72 (b) ₹144 (c) ₹96 (d) ₹49
2. 2.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 15 days (d) 27 days
3. 3.8 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 12 days (b) 11 days (c) 7 days (d) 13 days
4. 4.If 5 kites cost ₹120, how much do 10 kites cost? (a) ₹1200 (b) ₹264 (c) ₹240 (d) ₹125
5. 5.₹175 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹35 (b) ₹175 (c) ₹141 (d) ₹140
6. 6.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 1 day (c) 22 days (d) 11 days
7. 7.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 44 days (c) 45 days (d) 17 days
8. 8.If 9 notebooks cost ₹171, how much do 10 notebooks cost? (a) ₹209 (b) ₹1710 (c) ₹172 (d) ₹190
9. 9.₹63 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹9 (b) ₹55 (c) ₹63 (d) ₹54
10. 10.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 9 days (d) 7 days
11. 11.If 7 notebooks cost ₹147, how much do 2 notebooks cost? (a) ₹42 (b) ₹63 (c) ₹142 (d) ₹294
12. 12.If 6 mangoes cost ₹90, how much do 8 mangoes cost? (a) ₹92 (b) ₹720 (c) ₹135 (d) ₹120
13. 13.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 14 days (d) 20 days
14. 14.If 3 pens cost ₹66, how much do 5 pens cost? (a) ₹132 (b) ₹330 (c) ₹110 (d) ₹68
15. 15.₹90 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹30 (b) ₹60 (c) ₹45 (d) ₹90
16. 16.₹32 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹32 (b) ₹24 (c) ₹8 (d) ₹16
17. 17.₹250 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹250 (b) ₹125 (c) ₹25 (d) ₹225
18. 18.₹198 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹144 (b) ₹54 (c) ₹18 (d) ₹99
19. 19.If 5 notebooks cost ₹25, how much do 4 notebooks cost? (a) ₹100 (b) ₹25 (c) ₹24 (d) ₹20
20. 20.If 2 pens cost ₹14, how much do 9 pens cost? (a) ₹126 (b) ₹63 (c) ₹70 (d) ₹21
21. 21.If 4 mangoes cost ₹32, how much do 6 mangoes cost? (a) ₹56 (b) ₹48 (c) ₹192 (d) ₹34
22. 22.If 2 pens cost ₹38, how much do 7 pens cost? (a) ₹43 (b) ₹152 (c) ₹133 (d) ₹266
23. 23.4 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 14 days (b) 18 days (c) 10 days (d) 8 days
24. 24.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 45 days (c) 5 days (d) 21 days
25. 25.₹319 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹203 (b) ₹145 (c) ₹29 (d) ₹174
26. 26.6 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
27. 27.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 33 days (b) 5 days (c) 17 days (d) 34 days
28. 28.₹400 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹400 (b) ₹200 (c) ₹40 (d) ₹360
29. 29.If 5 kites cost ₹15, how much do 11 kites cost? (a) ₹165 (b) ₹33 (c) ₹21 (d) ₹36
30. 30.₹33 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹22 (b) ₹11 (c) ₹33 (d) ₹23
31. 31.₹406 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹29 (b) ₹203 (c) ₹261 (d) ₹145
32. 32.₹160 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹80 (b) ₹60 (c) ₹100 (d) ₹20
33. 33.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 7 days (d) 9 days
34. 34.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 22 days (b) 17 days (c) 13 days (d) 21 days
35. 35.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 17 days (c) 28 days (d) 11 days
36. 36.If 4 pens cost ₹20, how much do 6 pens cost? (a) ₹30 (b) ₹120 (c) ₹22 (d) ₹35
37. 37.If 9 kites cost ₹171, how much do 7 kites cost? (a) ₹133 (b) ₹169 (c) ₹1197 (d) ₹152
38. 38.₹234 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹117 (b) ₹72 (c) ₹162 (d) ₹18
39. 39.₹324 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹27 (b) ₹135 (c) ₹189 (d) ₹162
40. 40.₹165 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹66 (b) ₹33 (c) ₹132 (d) ₹99

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