Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 542 · 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. 1.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 14 days (b) 8 days (c) 15 days (d) 12 days
2. 2.₹276 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹138 (b) ₹46 (c) ₹230 (d) ₹276
3. 3.₹441 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹196 (b) ₹245 (c) ₹294 (d) ₹49
4. 4.If 2 pens cost ₹40, how much do 12 pens cost? (a) ₹480 (b) ₹260 (c) ₹50 (d) ₹240
5. 5.₹200 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹80 (b) ₹40 (c) ₹100 (d) ₹120
6. 6.3 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 11 days (d) 16 days
7. 7.If 2 mangoes cost ₹20, how much do 6 mangoes cost? (a) ₹70 (b) ₹24 (c) ₹120 (d) ₹60
8. 8.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 17 days (d) 13 days
9. 9.If 7 notebooks cost ₹140, how much do 3 notebooks cost? (a) ₹136 (b) ₹80 (c) ₹60 (d) ₹420
10. 10.9 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 7 days (d) 1 day
11. 11.If 2 mangoes cost ₹6, how much do 4 mangoes cost? (a) ₹12 (b) ₹8 (c) ₹24 (d) ₹15
12. 12.If 3 pens cost ₹57, how much do 9 pens cost? (a) ₹171 (b) ₹190 (c) ₹513 (d) ₹63
13. 13.₹91 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹13 (b) ₹39 (c) ₹65 (d) ₹52
14. 14.If 5 mangoes cost ₹125, how much do 6 mangoes cost? (a) ₹126 (b) ₹150 (c) ₹750 (d) ₹175
15. 15.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 13 days (c) 27 days (d) 3 days
16. 16.6 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 18 days (c) 14 days (d) 10 days
17. 17.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 21 days (d) 22 days
18. 18.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 22 days (c) 21 days (d) 13 days
19. 19.If 2 mangoes cost ₹34, how much do 9 mangoes cost? (a) ₹153 (b) ₹41 (c) ₹170 (d) ₹306
20. 20.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 2 days (c) 7 days (d) 8 days
21. 21.If 9 pens cost ₹27, how much do 4 pens cost? (a) ₹22 (b) ₹108 (c) ₹15 (d) ₹12
22. 22.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 11 days (c) 14 days (d) 16 days
23. 23.If 7 pens cost ₹28, how much do 6 pens cost? (a) ₹28 (b) ₹27 (c) ₹24 (d) ₹168
24. 24.If 6 notebooks cost ₹30, how much do 7 notebooks cost? (a) ₹40 (b) ₹210 (c) ₹31 (d) ₹35
25. 25.₹390 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹351 (b) ₹195 (c) ₹390 (d) ₹39
26. 26.₹360 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹210 (b) ₹180 (c) ₹30 (d) ₹150
27. 27.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 15 days (d) 7 days
28. 28.₹72 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹36 (b) ₹12 (c) ₹60 (d) ₹72
29. 29.If 9 pens cost ₹135, how much do 2 pens cost? (a) ₹30 (b) ₹45 (c) ₹128 (d) ₹270
30. 30.₹24 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹24 (b) ₹12 (c) ₹16 (d) ₹8
31. 31.If 4 notebooks cost ₹52, how much do 10 notebooks cost? (a) ₹58 (b) ₹143 (c) ₹130 (d) ₹520
32. 32.If 7 notebooks cost ₹70, how much do 9 notebooks cost? (a) ₹72 (b) ₹90 (c) ₹100 (d) ₹630
33. 33.If 3 kites cost ₹18, how much do 11 kites cost? (a) ₹26 (b) ₹198 (c) ₹66 (d) ₹72
34. 34.If 5 notebooks cost ₹70, how much do 2 notebooks cost? (a) ₹67 (b) ₹42 (c) ₹140 (d) ₹28
35. 35.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 3 days (c) 12 days (d) 2 days
36. 36.If 2 pens cost ₹40, how much do 6 pens cost? (a) ₹120 (b) ₹140 (c) ₹240 (d) ₹44
37. 37.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 8 days (c) 6 days (d) 7 days
38. 38.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 6 days (d) 24 days
39. 39.7 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 29 days (b) 16 days (c) 28 days (d) 8 days
40. 40.₹342 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹152 (b) ₹38 (c) ₹171 (d) ₹190

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