Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 437 · 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. 1.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 5 days (d) 4 days
2. 2.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 9 days (d) 49 days
3. 3.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 39 days (c) 19 days (d) 40 days
4. 4.₹190 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹114 (b) ₹95 (c) ₹38 (d) ₹76
5. 5.₹90 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹40 (b) ₹45 (c) ₹10 (d) ₹50
6. 6.If 8 pens cost ₹32, how much do 11 pens cost? (a) ₹35 (b) ₹352 (c) ₹48 (d) ₹44
7. 7.If 3 notebooks cost ₹63, how much do 8 notebooks cost? (a) ₹504 (b) ₹68 (c) ₹189 (d) ₹168
8. 8.If 5 pens cost ₹45, how much do 2 pens cost? (a) ₹90 (b) ₹42 (c) ₹18 (d) ₹27
9. 9.If 2 pens cost ₹24, how much do 4 pens cost? (a) ₹60 (b) ₹48 (c) ₹96 (d) ₹26
10. 10.If 3 mangoes cost ₹54, how much do 4 mangoes cost? (a) ₹90 (b) ₹216 (c) ₹55 (d) ₹72
11. 11.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 6 days (c) 4 days (d) 5 days
12. 12.If 3 mangoes cost ₹51, how much do 4 mangoes cost? (a) ₹68 (b) ₹52 (c) ₹204 (d) ₹85
13. 13.₹66 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹12 (b) ₹33 (c) ₹54 (d) ₹6
14. 14.If 5 mangoes cost ₹35, how much do 4 mangoes cost? (a) ₹35 (b) ₹140 (c) ₹28 (d) ₹34
15. 15.₹35 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹28 (b) ₹14 (c) ₹21 (d) ₹7
16. 16.If 2 pens cost ₹36, how much do 3 pens cost? (a) ₹108 (b) ₹54 (c) ₹72 (d) ₹37
17. 17.If 3 pens cost ₹15, how much do 10 pens cost? (a) ₹150 (b) ₹50 (c) ₹55 (d) ₹22
18. 18.₹198 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹18 (b) ₹99 (c) ₹126 (d) ₹72
19. 19.If 8 notebooks cost ₹192, how much do 3 notebooks cost? (a) ₹187 (b) ₹576 (c) ₹96 (d) ₹72
20. 20.If 6 kites cost ₹66, how much do 5 kites cost? (a) ₹65 (b) ₹330 (c) ₹66 (d) ₹55
21. 21.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 25 days (c) 5 days (d) 16 days
22. 22.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 7 days (c) 11 days (d) 15 days
23. 23.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 41 days (d) 40 days
24. 24.₹336 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹294 (b) ₹168 (c) ₹42 (d) ₹336
25. 25.₹147 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹84 (b) ₹105 (c) ₹63 (d) ₹21
26. 26.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 25 days (c) 13 days (d) 17 days
27. 27.If 7 notebooks cost ₹28, how much do 10 notebooks cost? (a) ₹31 (b) ₹44 (c) ₹40 (d) ₹280
28. 28.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 9 days (d) 2 days
29. 29.₹363 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹198 (b) ₹33 (c) ₹165 (d) ₹231
30. 30.If 2 notebooks cost ₹24, how much do 11 notebooks cost? (a) ₹144 (b) ₹264 (c) ₹132 (d) ₹33
31. 31.₹204 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹34 (b) ₹204 (c) ₹170 (d) ₹102
32. 32.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 18 days (d) 3 days
33. 33.If 9 pens cost ₹63, how much do 3 pens cost? (a) ₹28 (b) ₹57 (c) ₹189 (d) ₹21
34. 34.If 5 notebooks cost ₹20, how much do 4 notebooks cost? (a) ₹16 (b) ₹80 (c) ₹20 (d) ₹19
35. 35.₹56 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹40 (b) ₹16 (c) ₹8 (d) ₹28
36. 36.If 4 notebooks cost ₹80, how much do 11 notebooks cost? (a) ₹240 (b) ₹880 (c) ₹220 (d) ₹87
37. 37.₹533 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹410 (b) ₹369 (c) ₹41 (d) ₹164
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) 2 days (c) 9 days (d) 8 days
39. 39.8 workers can build a wall in 9 days. How many days will 4 workers take, working at the same speed? (a) 13 days (b) 19 days (c) 18 days (d) 5 days
40. 40.9 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 16 days (c) 15 days (d) 13 days

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