Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 745 · 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.₹207 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹46 (b) ₹184 (c) ₹161 (d) ₹23
2. 2.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 3 days (c) 7 days (d) 11 days
3. 3.If 5 kites cost ₹120, how much do 3 kites cost? (a) ₹72 (b) ₹96 (c) ₹360 (d) ₹118
4. 4.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 19 days (c) 35 days (d) 36 days
5. 5.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 49 days (d) 9 days
6. 6.If 2 notebooks cost ₹46, how much do 11 notebooks cost? (a) ₹55 (b) ₹276 (c) ₹253 (d) ₹506
7. 7.If 9 mangoes cost ₹81, how much do 3 mangoes cost? (a) ₹36 (b) ₹243 (c) ₹75 (d) ₹27
8. 8.If 3 notebooks cost ₹9, how much do 10 notebooks cost? (a) ₹33 (b) ₹90 (c) ₹16 (d) ₹30
9. 9.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 33 days (c) 17 days (d) 32 days
10. 10.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 45 days (b) 5 days (c) 9 days (d) 21 days
11. 11.If 4 notebooks cost ₹44, how much do 9 notebooks cost? (a) ₹110 (b) ₹396 (c) ₹99 (d) ₹49
12. 12.If 2 notebooks cost ₹44, how much do 8 notebooks cost? (a) ₹352 (b) ₹198 (c) ₹176 (d) ₹50
13. 13.₹80 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹30 (b) ₹40 (c) ₹10 (d) ₹50
14. 14.₹70 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹20 (b) ₹10 (c) ₹50 (d) ₹35
15. 15.If 4 pens cost ₹36, how much do 10 pens cost? (a) ₹42 (b) ₹99 (c) ₹360 (d) ₹90
16. 16.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 12 days (d) 5 days
17. 17.₹392 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹140 (b) ₹28 (c) ₹252 (d) ₹196
18. 18.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 5 days
19. 19.If 5 mangoes cost ₹20, how much do 6 mangoes cost? (a) ₹120 (b) ₹24 (c) ₹21 (d) ₹28
20. 20.₹176 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹48 (b) ₹16 (c) ₹128 (d) ₹88
21. 21.6 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
22. 22.₹224 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹16 (b) ₹112 (c) ₹80 (d) ₹144
23. 23.If 6 pens cost ₹60, how much do 2 pens cost? (a) ₹120 (b) ₹56 (c) ₹20 (d) ₹30
24. 24.If 8 kites cost ₹72, how much do 6 kites cost? (a) ₹432 (b) ₹63 (c) ₹54 (d) ₹70
25. 25.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 4 days (c) 14 days (d) 10 days
26. 26.If 4 mangoes cost ₹92, how much do 6 mangoes cost? (a) ₹138 (b) ₹552 (c) ₹161 (d) ₹94
27. 27.₹117 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹81 (b) ₹45 (c) ₹72 (d) ₹9
28. 28.₹286 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹143 (b) ₹182 (c) ₹104 (d) ₹26
29. 29.If 6 notebooks cost ₹72, how much do 5 notebooks cost? (a) ₹360 (b) ₹72 (c) ₹71 (d) ₹60
30. 30.If 9 notebooks cost ₹63, how much do 2 notebooks cost? (a) ₹14 (b) ₹56 (c) ₹126 (d) ₹21
31. 31.If 5 pens cost ₹25, how much do 6 pens cost? (a) ₹35 (b) ₹150 (c) ₹30 (d) ₹26
32. 32.₹130 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹52 (b) ₹78 (c) ₹65 (d) ₹26
33. 33.₹132 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹66 (b) ₹72 (c) ₹12 (d) ₹60
34. 34.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 9 days (d) 8 days
35. 35.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 7 days (d) 11 days
36. 36.If 7 kites cost ₹77, how much do 8 kites cost? (a) ₹78 (b) ₹88 (c) ₹616 (d) ₹99
37. 37.₹108 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹24 (b) ₹84 (c) ₹12 (d) ₹54
38. 38.6 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 12 days (d) 13 days
39. 39.If 8 notebooks cost ₹64, how much do 10 notebooks cost? (a) ₹88 (b) ₹80 (c) ₹640 (d) ₹66
40. 40.If 3 notebooks cost ₹33, how much do 6 notebooks cost? (a) ₹77 (b) ₹36 (c) ₹198 (d) ₹66

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