Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 981 · 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 2 pens cost ₹8, how much do 5 pens cost? (a) ₹11 (b) ₹40 (c) ₹20 (d) ₹24
2. 2.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 18 days (c) 5 days (d) 4 days
3. 3.If 8 pens cost ₹56, how much do 9 pens cost? (a) ₹57 (b) ₹63 (c) ₹70 (d) ₹504
4. 4.₹66 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹30 (b) ₹6 (c) ₹36 (d) ₹33
5. 5.If 5 notebooks cost ₹15, how much do 9 notebooks cost? (a) ₹19 (b) ₹27 (c) ₹135 (d) ₹30
6. 6.₹174 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹145 (b) ₹174 (c) ₹87 (d) ₹29
7. 7.If 2 kites cost ₹40, how much do 3 kites cost? (a) ₹60 (b) ₹41 (c) ₹80 (d) ₹120
8. 8.₹234 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹144 (b) ₹90 (c) ₹18 (d) ₹117
9. 9.If 8 mangoes cost ₹168, how much do 11 mangoes cost? (a) ₹171 (b) ₹252 (c) ₹1848 (d) ₹231
10. 10.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 17 days (d) 25 days
11. 11.₹363 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹297 (b) ₹330 (c) ₹33 (d) ₹66
12. 12.If 4 kites cost ₹60, how much do 5 kites cost? (a) ₹75 (b) ₹300 (c) ₹61 (d) ₹90
13. 13.If 6 mangoes cost ₹24, how much do 10 mangoes cost? (a) ₹44 (b) ₹40 (c) ₹240 (d) ₹28
14. 14.If 2 kites cost ₹26, how much do 6 kites cost? (a) ₹91 (b) ₹156 (c) ₹78 (d) ₹30
15. 15.₹180 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹180 (b) ₹150 (c) ₹30 (d) ₹90
16. 16.If 3 pens cost ₹66, how much do 7 pens cost? (a) ₹462 (b) ₹70 (c) ₹176 (d) ₹154
17. 17.₹104 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹52 (b) ₹64 (c) ₹8 (d) ₹40
18. 18.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 12 days (c) 4 days (d) 3 days
19. 19.If 6 notebooks cost ₹144, how much do 4 notebooks cost? (a) ₹120 (b) ₹142 (c) ₹96 (d) ₹576
20. 20.5 workers can build a wall in 12 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 24 days (c) 17 days (d) 6 days
21. 21.If 5 pens cost ₹45, how much do 10 pens cost? (a) ₹99 (b) ₹90 (c) ₹450 (d) ₹50
22. 22.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 12 days (d) 2 days
23. 23.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 13 days (d) 8 days
24. 24.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 16 days (d) 15 days
25. 25.₹24 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹24 (b) ₹6 (c) ₹12 (d) ₹18
26. 26.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 2 days (c) 4 days (d) 9 days
27. 27.If 8 notebooks cost ₹56, how much do 4 notebooks cost? (a) ₹52 (b) ₹35 (c) ₹224 (d) ₹28
28. 28.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 1 day (d) 11 days
29. 29.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 5 days (d) 9 days
30. 30.If 3 kites cost ₹21, how much do 6 kites cost? (a) ₹24 (b) ₹42 (c) ₹49 (d) ₹126
31. 31.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 9 days (d) 11 days
32. 32.₹186 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹93 (b) ₹31 (c) ₹155 (d) ₹186
33. 33.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 10 days (d) 5 days
34. 34.7 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 29 days (c) 16 days (d) 8 days
35. 35.If 2 mangoes cost ₹16, how much do 4 mangoes cost? (a) ₹64 (b) ₹18 (c) ₹32 (d) ₹40
36. 36.6 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 8 days (d) 4 days
37. 37.₹252 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹196 (b) ₹56 (c) ₹126 (d) ₹28
38. 38.₹240 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹20 (b) ₹120 (c) ₹100 (d) ₹140
39. 39.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 21 days (c) 5 days (d) 22 days
40. 40.₹473 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹215 (b) ₹258 (c) ₹301 (d) ₹43

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