Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 64 · 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. 1.9 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 7 days (d) 10 days
2. 2.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 22 days (b) 17 days (c) 21 days (d) 11 days
3. 3.If 5 kites cost ₹45, how much do 2 kites cost? (a) ₹27 (b) ₹90 (c) ₹18 (d) ₹42
4. 4.If 4 notebooks cost ₹60, how much do 8 notebooks cost? (a) ₹120 (b) ₹135 (c) ₹64 (d) ₹480
5. 5.If 3 mangoes cost ₹54, how much do 8 mangoes cost? (a) ₹144 (b) ₹432 (c) ₹162 (d) ₹59
6. 6.₹319 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹261 (b) ₹290 (c) ₹29 (d) ₹58
7. 7.If 9 mangoes cost ₹216, how much do 5 mangoes cost? (a) ₹1080 (b) ₹120 (c) ₹144 (d) ₹212
8. 8.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 36 days (c) 35 days (d) 15 days
9. 9.₹336 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹168 (b) ₹48 (c) ₹96 (d) ₹240
10. 10.If 3 pens cost ₹42, how much do 4 pens cost? (a) ₹168 (b) ₹70 (c) ₹43 (d) ₹56
11. 11.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 27 days (b) 1 day (c) 3 days (d) 17 days
12. 12.If 5 kites cost ₹85, how much do 6 kites cost? (a) ₹510 (b) ₹86 (c) ₹102 (d) ₹119
13. 13.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 18 days (c) 9 days (d) 8 days
14. 14.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 15 days (d) 3 days
15. 15.If 7 notebooks cost ₹154, how much do 9 notebooks cost? (a) ₹1386 (b) ₹156 (c) ₹220 (d) ₹198
16. 16.If 8 pens cost ₹88, how much do 4 pens cost? (a) ₹84 (b) ₹44 (c) ₹55 (d) ₹352
17. 17.6 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 14 days (b) 4 days (c) 2 days (d) 16 days
18. 18.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 13 days (c) 11 days (d) 12 days
19. 19.₹384 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹192 (b) ₹160 (c) ₹32 (d) ₹224
20. 20.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 3 days (c) 5 days (d) 4 days
21. 21.If 9 mangoes cost ₹117, how much do 12 mangoes cost? (a) ₹156 (b) ₹1404 (c) ₹120 (d) ₹169
22. 22.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 29 days (b) 13 days (c) 1 day (d) 28 days
23. 23.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 27 days (c) 13 days (d) 3 days
24. 24.If 2 mangoes cost ₹36, how much do 4 mangoes cost? (a) ₹38 (b) ₹90 (c) ₹144 (d) ₹72
25. 25.If 9 pens cost ₹108, how much do 7 pens cost? (a) ₹84 (b) ₹96 (c) ₹106 (d) ₹756
26. 26.If 2 notebooks cost ₹12, how much do 7 notebooks cost? (a) ₹84 (b) ₹42 (c) ₹48 (d) ₹17
27. 27.If 3 kites cost ₹60, how much do 12 kites cost? (a) ₹69 (b) ₹720 (c) ₹240 (d) ₹260
28. 28.₹99 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹44 (b) ₹66 (c) ₹11 (d) ₹55
29. 29.If 5 kites cost ₹90, how much do 9 kites cost? (a) ₹180 (b) ₹162 (c) ₹94 (d) ₹810
30. 30.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 19 days (c) 6 days (d) 12 days
31. 31.If 4 pens cost ₹88, how much do 5 pens cost? (a) ₹89 (b) ₹132 (c) ₹440 (d) ₹110
32. 32.5 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
33. 33.If 3 mangoes cost ₹21, how much do 4 mangoes cost? (a) ₹35 (b) ₹22 (c) ₹28 (d) ₹84
34. 34.If 5 pens cost ₹95, how much do 9 pens cost? (a) ₹855 (b) ₹99 (c) ₹190 (d) ₹171
35. 35.If 7 kites cost ₹161, how much do 6 kites cost? (a) ₹138 (b) ₹161 (c) ₹966 (d) ₹160
36. 36.If 6 pens cost ₹54, how much do 7 pens cost? (a) ₹378 (b) ₹63 (c) ₹55 (d) ₹72
37. 37.₹40 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹20 (b) ₹40 (c) ₹30 (d) ₹10
38. 38.4 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 18 days (b) 8 days (c) 14 days (d) 10 days
39. 39.If 5 pens cost ₹110, how much do 4 pens cost? (a) ₹110 (b) ₹440 (c) ₹109 (d) ₹88
40. 40.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 3 days (c) 13 days (d) 29 days

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