Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 586 · 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 6 kites cost ₹78, how much do 7 kites cost? (a) ₹104 (b) ₹79 (c) ₹91 (d) ₹546
2. 2.If 2 kites cost ₹38, how much do 10 kites cost? (a) ₹190 (b) ₹46 (c) ₹380 (d) ₹209
3. 3.If 9 kites cost ₹81, how much do 3 kites cost? (a) ₹243 (b) ₹36 (c) ₹27 (d) ₹75
4. 4.₹210 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹105 (b) ₹150 (c) ₹30 (d) ₹60
5. 5.If 4 notebooks cost ₹16, how much do 5 notebooks cost? (a) ₹20 (b) ₹17 (c) ₹80 (d) ₹24
6. 6.If 7 pens cost ₹105, how much do 5 pens cost? (a) ₹525 (b) ₹90 (c) ₹103 (d) ₹75
7. 7.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 39 days (b) 17 days (c) 9 days (d) 40 days
8. 8.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 16 days (d) 24 days
9. 9.If 3 pens cost ₹39, how much do 7 pens cost? (a) ₹104 (b) ₹91 (c) ₹43 (d) ₹273
10. 10.If 2 kites cost ₹24, how much do 3 kites cost? (a) ₹36 (b) ₹72 (c) ₹25 (d) ₹48
11. 11.₹598 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹46 (b) ₹299 (c) ₹368 (d) ₹230
12. 12.₹297 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹66 (b) ₹264 (c) ₹33 (d) ₹231
13. 13.₹147 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹98 (b) ₹147 (c) ₹99 (d) ₹49
14. 14.₹385 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹105 (b) ₹35 (c) ₹280 (d) ₹315
15. 15.₹432 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹180 (b) ₹216 (c) ₹252 (d) ₹36
16. 16.If 9 kites cost ₹153, how much do 3 kites cost? (a) ₹147 (b) ₹459 (c) ₹68 (d) ₹51
17. 17.₹48 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹24 (b) ₹6 (c) ₹30 (d) ₹18
18. 18.₹275 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹125 (b) ₹150 (c) ₹25 (d) ₹175
19. 19.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 26 days (d) 11 days
20. 20.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 4 days (d) 9 days
21. 21.₹481 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹333 (b) ₹185 (c) ₹37 (d) ₹296
22. 22.If 2 notebooks cost ₹48, how much do 9 notebooks cost? (a) ₹432 (b) ₹55 (c) ₹240 (d) ₹216
23. 23.If 7 notebooks cost ₹133, how much do 12 notebooks cost? (a) ₹247 (b) ₹228 (c) ₹1596 (d) ₹138
24. 24.5 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 19 days (d) 4 days
25. 25.If 2 kites cost ₹8, how much do 4 kites cost? (a) ₹16 (b) ₹10 (c) ₹32 (d) ₹20
26. 26.₹132 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹132 (b) ₹110 (c) ₹66 (d) ₹22
27. 27.₹57 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹57 (b) ₹19 (c) ₹39 (d) ₹38
28. 28.If 6 kites cost ₹78, how much do 4 kites cost? (a) ₹52 (b) ₹312 (c) ₹65 (d) ₹76
29. 29.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 7 days (c) 6 days (d) 8 days
30. 30.If 2 pens cost ₹34, how much do 4 pens cost? (a) ₹85 (b) ₹136 (c) ₹68 (d) ₹36
31. 31.₹325 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹100 (b) ₹25 (c) ₹250 (d) ₹225
32. 32.If 9 kites cost ₹171, how much do 3 kites cost? (a) ₹76 (b) ₹513 (c) ₹57 (d) ₹165
33. 33.If 5 pens cost ₹80, how much do 2 pens cost? (a) ₹160 (b) ₹77 (c) ₹32 (d) ₹48
34. 34.₹252 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹28 (b) ₹126 (c) ₹140 (d) ₹112
35. 35.₹64 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹32 (b) ₹8 (c) ₹64 (d) ₹56
36. 36.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 52 days (b) 53 days (c) 7 days (d) 19 days
37. 37.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 10 days (c) 14 days (d) 24 days
38. 38.If 2 kites cost ₹30, how much do 9 kites cost? (a) ₹135 (b) ₹150 (c) ₹37 (d) ₹270
39. 39.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 1 day (c) 16 days (d) 9 days
40. 40.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 6 days (d) 7 days

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