Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 806 · 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 8 notebooks cost ₹56, how much do 6 notebooks cost? (a) ₹54 (b) ₹336 (c) ₹42 (d) ₹49
2. 2.If 5 pens cost ₹20, how much do 9 pens cost? (a) ₹24 (b) ₹36 (c) ₹180 (d) ₹40
3. 3.If 4 kites cost ₹100, how much do 12 kites cost? (a) ₹108 (b) ₹1200 (c) ₹300 (d) ₹325
4. 4.If 9 pens cost ₹171, how much do 8 pens cost? (a) ₹170 (b) ₹152 (c) ₹1368 (d) ₹171
5. 5.₹432 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹96 (b) ₹336 (c) ₹216 (d) ₹48
6. 6.4 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 13 days (c) 8 days (d) 12 days
7. 7.₹209 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹133 (b) ₹152 (c) ₹19 (d) ₹76
8. 8.If 4 pens cost ₹16, how much do 11 pens cost? (a) ₹176 (b) ₹23 (c) ₹48 (d) ₹44
9. 9.₹216 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹120 (b) ₹108 (c) ₹96 (d) ₹24
10. 10.₹136 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹119 (b) ₹68 (c) ₹17 (d) ₹136
11. 11.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 17 days (d) 8 days
12. 12.₹342 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹152 (b) ₹171 (c) ₹190 (d) ₹38
13. 13.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 5 days (d) 4 days
14. 14.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 14 days (c) 9 days (d) 15 days
15. 15.₹533 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹328 (b) ₹41 (c) ₹369 (d) ₹205
16. 16.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 3 days (d) 2 days
17. 17.₹344 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹43 (b) ₹129 (c) ₹215 (d) ₹172
18. 18.If 5 pens cost ₹100, how much do 11 pens cost? (a) ₹220 (b) ₹106 (c) ₹1100 (d) ₹240
19. 19.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 13 days (b) 2 days (c) 16 days (d) 1 day
20. 20.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 1 day (c) 10 days (d) 16 days
21. 21.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 6 days (d) 5 days
22. 22.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 8 days (d) 7 days
23. 23.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 21 days (b) 9 days (c) 45 days (d) 5 days
24. 24.If 6 notebooks cost ₹144, how much do 4 notebooks cost? (a) ₹96 (b) ₹576 (c) ₹120 (d) ₹142
25. 25.If 8 mangoes cost ₹80, how much do 9 mangoes cost? (a) ₹720 (b) ₹100 (c) ₹81 (d) ₹90
26. 26.If 2 kites cost ₹30, how much do 5 kites cost? (a) ₹90 (b) ₹33 (c) ₹150 (d) ₹75
27. 27.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 21 days (c) 22 days (d) 13 days
28. 28.If 4 mangoes cost ₹68, how much do 5 mangoes cost? (a) ₹69 (b) ₹102 (c) ₹85 (d) ₹340
29. 29.₹462 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹165 (b) ₹297 (c) ₹33 (d) ₹231
30. 30.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 11 days (c) 8 days (d) 10 days
31. 31.If 7 notebooks cost ₹161, how much do 2 notebooks cost? (a) ₹322 (b) ₹69 (c) ₹156 (d) ₹46
32. 32.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 9 days (d) 10 days
33. 33.6 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 18 days (c) 14 days (d) 8 days
34. 34.If 9 notebooks cost ₹54, how much do 7 notebooks cost? (a) ₹378 (b) ₹42 (c) ₹52 (d) ₹48
35. 35.If 2 pens cost ₹18, how much do 6 pens cost? (a) ₹22 (b) ₹108 (c) ₹54 (d) ₹63
36. 36.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 18 days (b) 28 days (c) 7 days (d) 10 days
37. 37.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 13 days (c) 26 days (d) 27 days
38. 38.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 9 days (d) 2 days
39. 39.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 24 days (b) 15 days (c) 9 days (d) 6 days
40. 40.If 7 notebooks cost ₹133, how much do 11 notebooks cost? (a) ₹228 (b) ₹209 (c) ₹1463 (d) ₹137

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