Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 431 · 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 notebooks cost ₹78, how much do 5 notebooks cost? (a) ₹78 (b) ₹65 (c) ₹390 (d) ₹77
2. 2.₹560 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹280 (b) ₹360 (c) ₹200 (d) ₹40
3. 3.₹276 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹115 (b) ₹138 (c) ₹161 (d) ₹23
4. 4.If 3 mangoes cost ₹27, how much do 10 mangoes cost? (a) ₹34 (b) ₹270 (c) ₹90 (d) ₹99
5. 5.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 2 days (d) 3 days
6. 6.If 9 pens cost ₹198, how much do 3 pens cost? (a) ₹88 (b) ₹66 (c) ₹192 (d) ₹594
7. 7.If 6 mangoes cost ₹150, how much do 2 mangoes cost? (a) ₹146 (b) ₹300 (c) ₹50 (d) ₹75
8. 8.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 11 days (d) 8 days
9. 9.₹75 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹61 (b) ₹15 (c) ₹75 (d) ₹60
10. 10.If 8 kites cost ₹56, how much do 12 kites cost? (a) ₹60 (b) ₹84 (c) ₹672 (d) ₹91
11. 11.If 5 kites cost ₹75, how much do 8 kites cost? (a) ₹135 (b) ₹78 (c) ₹600 (d) ₹120
12. 12.If 8 mangoes cost ₹96, how much do 2 mangoes cost? (a) ₹24 (b) ₹36 (c) ₹90 (d) ₹192
13. 13.If 4 mangoes cost ₹68, how much do 8 mangoes cost? (a) ₹136 (b) ₹72 (c) ₹153 (d) ₹544
14. 14.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 9 days (d) 4 days
15. 15.8 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 20 days (b) 13 days (c) 21 days (d) 17 days
16. 16.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 10 days (c) 8 days (d) 9 days
17. 17.₹279 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹248 (b) ₹217 (c) ₹62 (d) ₹31
18. 18.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 21 days (b) 17 days (c) 13 days (d) 22 days
19. 19.8 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 12 days (c) 13 days (d) 7 days
20. 20.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 9 days (d) 4 days
21. 21.If 9 mangoes cost ₹99, how much do 10 mangoes cost? (a) ₹100 (b) ₹990 (c) ₹121 (d) ₹110
22. 22.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 3 days
23. 23.If 3 pens cost ₹60, how much do 7 pens cost? (a) ₹64 (b) ₹420 (c) ₹140 (d) ₹160
24. 24.₹65 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹13 (b) ₹26 (c) ₹52 (d) ₹39
25. 25.If 8 kites cost ₹112, how much do 5 kites cost? (a) ₹70 (b) ₹109 (c) ₹84 (d) ₹560
26. 26.If 2 kites cost ₹26, how much do 7 kites cost? (a) ₹182 (b) ₹104 (c) ₹31 (d) ₹91
27. 27.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 4 days (d) 11 days
28. 28.8 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 19 days (d) 11 days
29. 29.₹240 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹72 (b) ₹24 (c) ₹168 (d) ₹120
30. 30.8 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) 10 days (d) 9 days
31. 31.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 9 days (d) 1 day
32. 32.6 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 16 days (c) 4 days (d) 14 days
33. 33.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 16 days (c) 25 days (d) 4 days
34. 34.₹54 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹12 (b) ₹27 (c) ₹42 (d) ₹6
35. 35.If 2 mangoes cost ₹10, how much do 7 mangoes cost? (a) ₹35 (b) ₹40 (c) ₹15 (d) ₹70
36. 36.If 3 notebooks cost ₹75, how much do 12 notebooks cost? (a) ₹325 (b) ₹900 (c) ₹300 (d) ₹84
37. 37.If 9 pens cost ₹54, how much do 4 pens cost? (a) ₹24 (b) ₹49 (c) ₹30 (d) ₹216
38. 38.If 5 kites cost ₹15, how much do 4 kites cost? (a) ₹15 (b) ₹12 (c) ₹14 (d) ₹60
39. 39.₹396 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹176 (b) ₹198 (c) ₹220 (d) ₹44
40. 40.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 12 days (d) 16 days

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