Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 624 · 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.₹133 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹38 (b) ₹95 (c) ₹19 (d) ₹114
2. 2.₹45 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹45 (b) ₹31 (c) ₹15 (d) ₹30
3. 3.₹65 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹45 (b) ₹5 (c) ₹50 (d) ₹20
4. 4.₹420 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹35 (b) ₹210 (c) ₹175 (d) ₹245
5. 5.If 7 kites cost ₹21, how much do 11 kites cost? (a) ₹231 (b) ₹25 (c) ₹33 (d) ₹36
6. 6.₹407 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹37 (b) ₹259 (c) ₹148 (d) ₹296
7. 7.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 7 days (d) 4 days
8. 8.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 12 days
9. 9.If 6 pens cost ₹72, how much do 3 pens cost? (a) ₹36 (b) ₹69 (c) ₹48 (d) ₹216
10. 10.If 4 pens cost ₹96, how much do 3 pens cost? (a) ₹288 (b) ₹96 (c) ₹95 (d) ₹72
11. 11.If 8 pens cost ₹112, how much do 7 pens cost? (a) ₹111 (b) ₹98 (c) ₹784 (d) ₹112
12. 12.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 12 days (b) 5 days (c) 16 days (d) 4 days
13. 13.If 8 pens cost ₹176, how much do 10 pens cost? (a) ₹1760 (b) ₹242 (c) ₹178 (d) ₹220
14. 14.₹144 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹12 (b) ₹72 (c) ₹60 (d) ₹84
15. 15.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 33 days (b) 15 days (c) 7 days (d) 34 days
16. 16.₹121 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹11 (b) ₹22 (c) ₹110 (d) ₹99
17. 17.If 9 pens cost ₹72, how much do 11 pens cost? (a) ₹792 (b) ₹74 (c) ₹88 (d) ₹96
18. 18.If 3 pens cost ₹75, how much do 9 pens cost? (a) ₹675 (b) ₹81 (c) ₹225 (d) ₹250
19. 19.₹189 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹135 (b) ₹162 (c) ₹27 (d) ₹54
20. 20.If 9 notebooks cost ₹99, how much do 2 notebooks cost? (a) ₹92 (b) ₹22 (c) ₹198 (d) ₹33
21. 21.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹7 (b) ₹56 (c) ₹35 (d) ₹63
22. 22.₹440 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹240 (b) ₹40 (c) ₹220 (d) ₹200
23. 23.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 9 days (d) 14 days
24. 24.If 6 mangoes cost ₹90, how much do 3 mangoes cost? (a) ₹270 (b) ₹60 (c) ₹87 (d) ₹45
25. 25.If 3 mangoes cost ₹30, how much do 4 mangoes cost? (a) ₹120 (b) ₹31 (c) ₹50 (d) ₹40
26. 26.If 5 pens cost ₹75, how much do 12 pens cost? (a) ₹82 (b) ₹180 (c) ₹900 (d) ₹195
27. 27.If 3 mangoes cost ₹21, how much do 12 mangoes cost? (a) ₹252 (b) ₹30 (c) ₹91 (d) ₹84
28. 28.5 workers can build a wall in 12 days. How many days will 10 workers take, working at the same speed? (a) 17 days (b) 24 days (c) 7 days (d) 6 days
29. 29.If 7 kites cost ₹154, how much do 9 kites cost? (a) ₹1386 (b) ₹198 (c) ₹220 (d) ₹156
30. 30.₹128 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹80 (b) ₹64 (c) ₹16 (d) ₹48
31. 31.If 3 kites cost ₹36, how much do 6 kites cost? (a) ₹216 (b) ₹39 (c) ₹72 (d) ₹84
32. 32.₹50 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹15 (b) ₹35 (c) ₹5 (d) ₹25
33. 33.7 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) 7 days (d) 6 days
34. 34.₹84 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹84 (b) ₹42 (c) ₹72 (d) ₹12
35. 35.If 6 mangoes cost ₹72, how much do 3 mangoes cost? (a) ₹69 (b) ₹216 (c) ₹36 (d) ₹48
36. 36.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 6 days (d) 9 days
37. 37.If 7 pens cost ₹56, how much do 10 pens cost? (a) ₹560 (b) ₹59 (c) ₹80 (d) ₹88
38. 38.If 9 mangoes cost ₹108, how much do 10 mangoes cost? (a) ₹132 (b) ₹1080 (c) ₹109 (d) ₹120
39. 39.If 2 mangoes cost ₹30, how much do 5 mangoes cost? (a) ₹150 (b) ₹33 (c) ₹90 (d) ₹75
40. 40.If 8 pens cost ₹184, how much do 10 pens cost? (a) ₹186 (b) ₹230 (c) ₹253 (d) ₹1840

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