Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 35 · 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 4 mangoes cost ₹52, how much do 7 mangoes cost? (a) ₹91 (b) ₹104 (c) ₹55 (d) ₹364
2. 2.₹400 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹200 (b) ₹40 (c) ₹120 (d) ₹280
3. 3.If 4 kites cost ₹80, how much do 8 kites cost? (a) ₹640 (b) ₹180 (c) ₹84 (d) ₹160
4. 4.If 8 mangoes cost ₹136, how much do 5 mangoes cost? (a) ₹680 (b) ₹133 (c) ₹85 (d) ₹102
5. 5.₹245 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹210 (b) ₹211 (c) ₹35 (d) ₹245
6. 6.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 2 days (c) 3 days (d) 8 days
7. 7.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 19 days (d) 11 days
8. 8.₹203 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹29 (b) ₹175 (c) ₹203 (d) ₹174
9. 9.9 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 25 days (c) 24 days (d) 14 days
10. 10.₹320 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹280 (b) ₹160 (c) ₹40 (d) ₹320
11. 11.₹110 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹60 (b) ₹10 (c) ₹50 (d) ₹55
12. 12.₹253 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹23 (b) ₹69 (c) ₹207 (d) ₹184
13. 13.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 9 days (d) 10 days
14. 14.If 6 kites cost ₹18, how much do 10 kites cost? (a) ₹180 (b) ₹30 (c) ₹33 (d) ₹22
15. 15.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 28 days (c) 7 days (d) 16 days
16. 16.₹115 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹92 (b) ₹23 (c) ₹93 (d) ₹115
17. 17.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 31 days (b) 17 days (c) 13 days (d) 30 days
18. 18.8 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 25 days (b) 18 days (c) 12 days (d) 24 days
19. 19.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 15 days
20. 20.₹550 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹250 (b) ₹50 (c) ₹275 (d) ₹300
21. 21.₹160 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹64 (b) ₹32 (c) ₹80 (d) ₹96
22. 22.₹110 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹11 (b) ₹77 (c) ₹55 (d) ₹33
23. 23.₹324 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹144 (b) ₹36 (c) ₹180 (d) ₹162
24. 24.If 9 kites cost ₹180, how much do 7 kites cost? (a) ₹140 (b) ₹160 (c) ₹1260 (d) ₹178
25. 25.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 17 days (d) 5 days
26. 26.₹120 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹75 (b) ₹60 (c) ₹45 (d) ₹15
27. 27.If 8 notebooks cost ₹176, how much do 4 notebooks cost? (a) ₹704 (b) ₹172 (c) ₹110 (d) ₹88
28. 28.If 4 kites cost ₹44, how much do 2 kites cost? (a) ₹33 (b) ₹42 (c) ₹22 (d) ₹88
29. 29.₹360 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹45 (b) ₹360 (c) ₹315 (d) ₹180
30. 30.₹72 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹36 (b) ₹6 (c) ₹30 (d) ₹42
31. 31.If 8 mangoes cost ₹192, how much do 6 mangoes cost? (a) ₹190 (b) ₹144 (c) ₹168 (d) ₹1152
32. 32.₹224 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹112 (b) ₹96 (c) ₹32 (d) ₹128
33. 33.If 9 pens cost ₹27, how much do 8 pens cost? (a) ₹216 (b) ₹27 (c) ₹24 (d) ₹26
34. 34.If 6 kites cost ₹96, how much do 2 kites cost? (a) ₹48 (b) ₹32 (c) ₹92 (d) ₹192
35. 35.If 8 mangoes cost ₹32, how much do 7 mangoes cost? (a) ₹224 (b) ₹32 (c) ₹31 (d) ₹28
36. 36.If 4 pens cost ₹72, how much do 6 pens cost? (a) ₹74 (b) ₹108 (c) ₹432 (d) ₹126
37. 37.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 13 days (c) 8 days (d) 7 days
38. 38.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 12 days (d) 10 days
39. 39.If 6 mangoes cost ₹72, how much do 3 mangoes cost? (a) ₹69 (b) ₹36 (c) ₹48 (d) ₹216
40. 40.₹88 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹8 (b) ₹24 (c) ₹64 (d) ₹44

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