Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 242 · 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. 1.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 12 days (d) 7 days
2. 2.₹297 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹189 (b) ₹27 (c) ₹216 (d) ₹108
3. 3.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 3 days
4. 4.₹104 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹40 (b) ₹52 (c) ₹8 (d) ₹64
5. 5.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 3 days (d) 4 days
6. 6.₹68 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹34 (b) ₹17 (c) ₹68 (d) ₹51
7. 7.If 3 pens cost ₹66, how much do 8 pens cost? (a) ₹528 (b) ₹198 (c) ₹71 (d) ₹176
8. 8.If 9 notebooks cost ₹135, how much do 5 notebooks cost? (a) ₹131 (b) ₹75 (c) ₹675 (d) ₹90
9. 9.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 25 days (c) 4 days (d) 16 days
10. 10.If 7 pens cost ₹161, how much do 8 pens cost? (a) ₹207 (b) ₹1288 (c) ₹162 (d) ₹184
11. 11.If 3 notebooks cost ₹75, how much do 2 notebooks cost? (a) ₹150 (b) ₹75 (c) ₹74 (d) ₹50
12. 12.If 4 kites cost ₹68, how much do 6 kites cost? (a) ₹408 (b) ₹102 (c) ₹119 (d) ₹70
13. 13.₹120 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹24 (b) ₹96 (c) ₹120 (d) ₹60
14. 14.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 6 days (c) 7 days (d) 8 days
15. 15.If 3 mangoes cost ₹69, how much do 2 mangoes cost? (a) ₹138 (b) ₹46 (c) ₹68 (d) ₹69
16. 16.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 9 days (c) 8 days (d) 7 days
17. 17.If 7 kites cost ₹126, how much do 11 kites cost? (a) ₹1386 (b) ₹130 (c) ₹198 (d) ₹216
18. 18.If 5 pens cost ₹125, how much do 7 pens cost? (a) ₹200 (b) ₹175 (c) ₹127 (d) ₹875
19. 19.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 1 day (d) 2 days
20. 20.₹124 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹93 (b) ₹31 (c) ₹124 (d) ₹62
21. 21.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 8 days (d) 6 days
22. 22.₹286 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹26 (b) ₹143 (c) ₹104 (d) ₹182
23. 23.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 1 day (b) 3 days (c) 8 days (d) 2 days
24. 24.₹140 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹10 (b) ₹50 (c) ₹70 (d) ₹90
25. 25.₹117 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹13 (b) ₹26 (c) ₹91 (d) ₹104
26. 26.₹45 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹5 (b) ₹30 (c) ₹20 (d) ₹25
27. 27.₹344 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹301 (b) ₹172 (c) ₹43 (d) ₹344
28. 28.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 16 days (d) 5 days
29. 29.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 7 days (c) 11 days (d) 18 days
30. 30.₹182 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹91 (b) ₹26 (c) ₹156 (d) ₹182
31. 31.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 26 days (c) 27 days (d) 15 days
32. 32.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 53 days (b) 19 days (c) 7 days (d) 52 days
33. 33.If 6 notebooks cost ₹150, how much do 5 notebooks cost? (a) ₹125 (b) ₹150 (c) ₹750 (d) ₹149
34. 34.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 25 days (b) 13 days (c) 9 days (d) 17 days
35. 35.₹429 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹273 (b) ₹156 (c) ₹39 (d) ₹312
36. 36.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 12 days (c) 4 days (d) 16 days
37. 37.₹224 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹64 (b) ₹160 (c) ₹32 (d) ₹112
38. 38.5 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 13 days (d) 9 days
39. 39.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 2 days (b) 12 days (c) 3 days (d) 18 days
40. 40.₹243 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹162 (b) ₹27 (c) ₹108 (d) ₹135

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