Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 909 · 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 7 kites cost ₹140, how much do 8 kites cost? (a) ₹1120 (b) ₹180 (c) ₹141 (d) ₹160
2. 2.If 6 mangoes cost ₹78, how much do 7 mangoes cost? (a) ₹104 (b) ₹546 (c) ₹91 (d) ₹79
3. 3.If 3 pens cost ₹75, how much do 2 pens cost? (a) ₹150 (b) ₹50 (c) ₹75 (d) ₹74
4. 4.If 4 kites cost ₹52, how much do 10 kites cost? (a) ₹130 (b) ₹143 (c) ₹520 (d) ₹58
5. 5.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 12 days (c) 13 days (d) 11 days
6. 6.If 8 pens cost ₹72, how much do 6 pens cost? (a) ₹70 (b) ₹54 (c) ₹63 (d) ₹432
7. 7.If 6 kites cost ₹96, how much do 8 kites cost? (a) ₹144 (b) ₹768 (c) ₹98 (d) ₹128
8. 8.If 4 mangoes cost ₹100, how much do 5 mangoes cost? (a) ₹101 (b) ₹125 (c) ₹500 (d) ₹150
9. 9.6 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 2 days (d) 7 days
10. 10.6 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 13 days (c) 3 days (d) 9 days
11. 11.If 9 mangoes cost ₹171, how much do 2 mangoes cost? (a) ₹57 (b) ₹38 (c) ₹164 (d) ₹342
12. 12.If 8 notebooks cost ₹168, how much do 7 notebooks cost? (a) ₹167 (b) ₹1176 (c) ₹168 (d) ₹147
13. 13.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 18 days (d) 28 days
14. 14.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 14 days (d) 9 days
15. 15.If 9 mangoes cost ₹36, how much do 12 mangoes cost? (a) ₹52 (b) ₹432 (c) ₹39 (d) ₹48
16. 16.₹176 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹88 (b) ₹176 (c) ₹132 (d) ₹44
17. 17.₹45 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹45 (b) ₹31 (c) ₹30 (d) ₹15
18. 18.If 5 kites cost ₹25, how much do 3 kites cost? (a) ₹75 (b) ₹20 (c) ₹23 (d) ₹15
19. 19.₹300 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹270 (b) ₹300 (c) ₹150 (d) ₹30
20. 20.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 6 days (d) 7 days
21. 21.If 5 notebooks cost ₹50, how much do 6 notebooks cost? (a) ₹60 (b) ₹70 (c) ₹300 (d) ₹51
22. 22.If 4 notebooks cost ₹80, how much do 11 notebooks cost? (a) ₹220 (b) ₹880 (c) ₹87 (d) ₹240
23. 23.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 10 days (c) 12 days (d) 3 days
24. 24.If 5 pens cost ₹50, how much do 4 pens cost? (a) ₹200 (b) ₹50 (c) ₹49 (d) ₹40
25. 25.₹360 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹315 (b) ₹360 (c) ₹180 (d) ₹45
26. 26.₹160 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹112 (b) ₹48 (c) ₹16 (d) ₹80
27. 27.₹156 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹39 (b) ₹117 (c) ₹156 (d) ₹78
28. 28.If 5 kites cost ₹115, how much do 12 kites cost? (a) ₹122 (b) ₹1380 (c) ₹299 (d) ₹276
29. 29.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 24 days (b) 12 days (c) 25 days (d) 4 days
30. 30.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 15 days (c) 11 days (d) 16 days
31. 31.If 4 mangoes cost ₹28, how much do 2 mangoes cost? (a) ₹56 (b) ₹14 (c) ₹21 (d) ₹26
32. 32.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 27 days (b) 17 days (c) 1 day (d) 3 days
33. 33.₹170 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹85 (b) ₹68 (c) ₹102 (d) ₹34
34. 34.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 8 days (d) 7 days
35. 35.₹60 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹30 (b) ₹54 (c) ₹60 (d) ₹6
36. 36.₹546 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹168 (b) ₹378 (c) ₹42 (d) ₹273
37. 37.₹136 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹51 (b) ₹17 (c) ₹85 (d) ₹68
38. 38.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 4 days (d) 5 days
39. 39.If 7 notebooks cost ₹21, how much do 11 notebooks cost? (a) ₹36 (b) ₹33 (c) ₹25 (d) ₹231
40. 40.If 6 pens cost ₹126, how much do 4 pens cost? (a) ₹84 (b) ₹124 (c) ₹105 (d) ₹504

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