Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 704 · 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.₹528 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹264 (b) ₹44 (c) ₹308 (d) ₹220
2. 2.If 5 notebooks cost ₹105, how much do 8 notebooks cost? (a) ₹108 (b) ₹840 (c) ₹189 (d) ₹168
3. 3.If 2 kites cost ₹14, how much do 10 kites cost? (a) ₹70 (b) ₹140 (c) ₹77 (d) ₹22
4. 4.If 3 pens cost ₹72, how much do 9 pens cost? (a) ₹240 (b) ₹216 (c) ₹648 (d) ₹78
5. 5.If 3 pens cost ₹63, how much do 5 pens cost? (a) ₹126 (b) ₹105 (c) ₹315 (d) ₹65
6. 6.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 5 days (d) 3 days
7. 7.If 4 pens cost ₹68, how much do 10 pens cost? (a) ₹680 (b) ₹170 (c) ₹74 (d) ₹187
8. 8.4 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
9. 9.If 3 mangoes cost ₹12, how much do 12 mangoes cost? (a) ₹21 (b) ₹52 (c) ₹144 (d) ₹48
10. 10.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 43 days (b) 42 days (c) 7 days (d) 17 days
11. 11.If 6 notebooks cost ₹126, how much do 9 notebooks cost? (a) ₹210 (b) ₹189 (c) ₹129 (d) ₹1134
12. 12.If 8 pens cost ₹88, how much do 4 pens cost? (a) ₹44 (b) ₹352 (c) ₹55 (d) ₹84
13. 13.If 2 pens cost ₹20, how much do 4 pens cost? (a) ₹50 (b) ₹80 (c) ₹40 (d) ₹22
14. 14.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 20 days (c) 21 days (d) 11 days
15. 15.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 1 day (b) 2 days (c) 7 days (d) 8 days
16. 16.If 4 notebooks cost ₹88, how much do 11 notebooks cost? (a) ₹968 (b) ₹242 (c) ₹95 (d) ₹264
17. 17.If 4 pens cost ₹64, how much do 5 pens cost? (a) ₹65 (b) ₹80 (c) ₹320 (d) ₹96
18. 18.If 5 notebooks cost ₹65, how much do 8 notebooks cost? (a) ₹117 (b) ₹104 (c) ₹520 (d) ₹68
19. 19.₹98 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹7 (b) ₹49 (c) ₹35 (d) ₹63
20. 20.₹160 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹20 (b) ₹60 (c) ₹80 (d) ₹100
21. 21.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 16 days (d) 14 days
22. 22.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 12 days (c) 7 days (d) 13 days
23. 23.If 6 pens cost ₹78, how much do 3 pens cost? (a) ₹234 (b) ₹75 (c) ₹39 (d) ₹52
24. 24.6 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 20 days (b) 7 days (c) 5 days (d) 13 days
25. 25.If 9 mangoes cost ₹117, how much do 8 mangoes cost? (a) ₹117 (b) ₹936 (c) ₹104 (d) ₹116
26. 26.If 3 pens cost ₹66, how much do 8 pens cost? (a) ₹71 (b) ₹176 (c) ₹528 (d) ₹198
27. 27.₹126 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹126 (b) ₹108 (c) ₹63 (d) ₹18
28. 28.₹120 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹60 (b) ₹10 (c) ₹50 (d) ₹70
29. 29.₹55 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹35 (b) ₹40 (c) ₹20 (d) ₹5
30. 30.₹66 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹33 (b) ₹30 (c) ₹6 (d) ₹36
31. 31.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 6 days (c) 5 days (d) 4 days
32. 32.If 7 pens cost ₹161, how much do 11 pens cost? (a) ₹253 (b) ₹276 (c) ₹1771 (d) ₹165
33. 33.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 49 days (b) 4 days (c) 19 days (d) 9 days
34. 34.If 5 mangoes cost ₹80, how much do 9 mangoes cost? (a) ₹84 (b) ₹160 (c) ₹144 (d) ₹720
35. 35.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 14 days (b) 5 days (c) 20 days (d) 6 days
36. 36.₹209 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹19 (b) ₹38 (c) ₹190 (d) ₹171
37. 37.3 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 16 days (d) 4 days
38. 38.If 6 pens cost ₹108, how much do 3 pens cost? (a) ₹105 (b) ₹54 (c) ₹324 (d) ₹72
39. 39.If 9 kites cost ₹27, how much do 7 kites cost? (a) ₹25 (b) ₹189 (c) ₹24 (d) ₹21
40. 40.If 9 pens cost ₹189, how much do 10 pens cost? (a) ₹231 (b) ₹190 (c) ₹1890 (d) ₹210

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