Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 246 · 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.₹352 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹160 (b) ₹176 (c) ₹32 (d) ₹192
2. 2.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 21 days (d) 1 day
3. 3.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 25 days (d) 17 days
4. 4.If 2 pens cost ₹8, how much do 11 pens cost? (a) ₹48 (b) ₹44 (c) ₹88 (d) ₹17
5. 5.If 7 mangoes cost ₹140, how much do 10 mangoes cost? (a) ₹143 (b) ₹220 (c) ₹1400 (d) ₹200
6. 6.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 3 days (d) 2 days
7. 7.If 5 kites cost ₹35, how much do 11 kites cost? (a) ₹84 (b) ₹385 (c) ₹77 (d) ₹41
8. 8.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 8 days (d) 15 days
9. 9.If 7 pens cost ₹161, how much do 4 pens cost? (a) ₹158 (b) ₹115 (c) ₹92 (d) ₹644
10. 10.₹77 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹28 (b) ₹56 (c) ₹49 (d) ₹7
11. 11.₹88 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹8 (b) ₹40 (c) ₹44 (d) ₹48
12. 12.6 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 4 days (c) 9 days (d) 10 days
13. 13.₹294 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹245 (b) ₹294 (c) ₹49 (d) ₹147
14. 14.If 5 kites cost ₹55, how much do 2 kites cost? (a) ₹33 (b) ₹110 (c) ₹22 (d) ₹52
15. 15.₹462 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹231 (b) ₹33 (c) ₹165 (d) ₹297
16. 16.₹225 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹125 (b) ₹25 (c) ₹100 (d) ₹150
17. 17.If 6 mangoes cost ₹36, how much do 4 mangoes cost? (a) ₹34 (b) ₹30 (c) ₹24 (d) ₹144
18. 18.If 5 notebooks cost ₹40, how much do 3 notebooks cost? (a) ₹32 (b) ₹120 (c) ₹24 (d) ₹38
19. 19.If 6 kites cost ₹84, how much do 4 kites cost? (a) ₹336 (b) ₹82 (c) ₹70 (d) ₹56
20. 20.₹240 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹20 (b) ₹100 (c) ₹120 (d) ₹140
21. 21.₹126 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹63 (b) ₹81 (c) ₹45 (d) ₹9
22. 22.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 1 day (d) 3 days
23. 23.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 24 days (c) 6 days (d) 16 days
24. 24.If 2 notebooks cost ₹14, how much do 6 notebooks cost? (a) ₹84 (b) ₹49 (c) ₹18 (d) ₹42
25. 25.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 10 days (c) 18 days (d) 7 days
26. 26.₹198 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹44 (b) ₹99 (c) ₹22 (d) ₹154
27. 27.₹216 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹96 (b) ₹108 (c) ₹120 (d) ₹24
28. 28.If 7 pens cost ₹21, how much do 4 pens cost? (a) ₹84 (b) ₹18 (c) ₹12 (d) ₹15
29. 29.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 20 days (c) 14 days (d) 16 days
30. 30.If 9 mangoes cost ₹81, how much do 3 mangoes cost? (a) ₹75 (b) ₹36 (c) ₹243 (d) ₹27
31. 31.If 5 mangoes cost ₹105, how much do 2 mangoes cost? (a) ₹42 (b) ₹63 (c) ₹210 (d) ₹102
32. 32.₹301 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹259 (b) ₹301 (c) ₹258 (d) ₹43
33. 33.If 4 mangoes cost ₹60, how much do 9 mangoes cost? (a) ₹540 (b) ₹65 (c) ₹150 (d) ₹135
34. 34.If 7 notebooks cost ₹84, how much do 3 notebooks cost? (a) ₹36 (b) ₹80 (c) ₹252 (d) ₹48
35. 35.If 9 pens cost ₹162, how much do 6 pens cost? (a) ₹972 (b) ₹108 (c) ₹159 (d) ₹126
36. 36.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 48 days (c) 6 days (d) 3 days
37. 37.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 19 days (b) 28 days (c) 11 days (d) 27 days
38. 38.₹24 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹24 (b) ₹12 (c) ₹18 (d) ₹6
39. 39.₹550 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹50 (b) ₹275 (c) ₹150 (d) ₹400
40. 40.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 15 days (d) 14 days

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