Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 554 · 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 mangoes cost ₹28, how much do 5 mangoes cost? (a) ₹84 (b) ₹31 (c) ₹70 (d) ₹140
2. 2.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 16 days (c) 9 days (d) 15 days
3. 3.If 8 kites cost ₹24, how much do 7 kites cost? (a) ₹21 (b) ₹24 (c) ₹168 (d) ₹23
4. 4.If 2 pens cost ₹34, how much do 3 pens cost? (a) ₹68 (b) ₹51 (c) ₹35 (d) ₹102
5. 5.If 4 notebooks cost ₹32, how much do 7 notebooks cost? (a) ₹224 (b) ₹56 (c) ₹35 (d) ₹64
6. 6.₹54 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹6 (b) ₹30 (c) ₹24 (d) ₹27
7. 7.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 15 days (c) 7 days (d) 6 days
8. 8.If 2 pens cost ₹10, how much do 7 pens cost? (a) ₹70 (b) ₹40 (c) ₹15 (d) ₹35
9. 9.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 13 days (b) 10 days (c) 8 days (d) 9 days
10. 10.If 4 pens cost ₹16, how much do 5 pens cost? (a) ₹20 (b) ₹17 (c) ₹24 (d) ₹80
11. 11.₹132 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹108 (b) ₹24 (c) ₹66 (d) ₹12
12. 12.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 15 days (c) 14 days (d) 10 days
13. 13.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 33 days (b) 34 days (c) 17 days (d) 5 days
14. 14.₹352 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹176 (b) ₹32 (c) ₹224 (d) ₹128
15. 15.If 5 pens cost ₹30, how much do 9 pens cost? (a) ₹34 (b) ₹270 (c) ₹54 (d) ₹60
16. 16.₹180 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹140 (b) ₹40 (c) ₹20 (d) ₹90
17. 17.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 21 days (d) 45 days
18. 18.₹234 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹26 (b) ₹208 (c) ₹234 (d) ₹117
19. 19.6 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 7 days (c) 11 days (d) 17 days
20. 20.If 5 notebooks cost ₹85, how much do 4 notebooks cost? (a) ₹85 (b) ₹84 (c) ₹68 (d) ₹340
21. 21.If 3 pens cost ₹15, how much do 4 pens cost? (a) ₹60 (b) ₹20 (c) ₹25 (d) ₹16
22. 22.₹96 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹12 (b) ₹48 (c) ₹36 (d) ₹60
23. 23.₹231 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹33 (b) ₹198 (c) ₹199 (d) ₹231
24. 24.If 4 notebooks cost ₹92, how much do 12 notebooks cost? (a) ₹100 (b) ₹276 (c) ₹299 (d) ₹1104
25. 25.If 5 mangoes cost ₹80, how much do 3 mangoes cost? (a) ₹48 (b) ₹78 (c) ₹64 (d) ₹240
26. 26.₹39 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹13 (b) ₹39 (c) ₹27 (d) ₹26
27. 27.₹64 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹40 (b) ₹8 (c) ₹24 (d) ₹32
28. 28.If 6 notebooks cost ₹54, how much do 12 notebooks cost? (a) ₹648 (b) ₹117 (c) ₹108 (d) ₹60
29. 29.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 16 days (c) 4 days (d) 10 days
30. 30.₹28 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹21 (b) ₹14 (c) ₹7 (d) ₹28
31. 31.If 7 notebooks cost ₹28, how much do 6 notebooks cost? (a) ₹24 (b) ₹27 (c) ₹28 (d) ₹168
32. 32.If 5 kites cost ₹15, how much do 9 kites cost? (a) ₹19 (b) ₹30 (c) ₹135 (d) ₹27
33. 33.₹45 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹5 (b) ₹41 (c) ₹45 (d) ₹40
34. 34.If 5 pens cost ₹55, how much do 3 pens cost? (a) ₹44 (b) ₹165 (c) ₹33 (d) ₹53
35. 35.4 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 7 days (d) 6 days
36. 36.9 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 46 days (b) 17 days (c) 3 days (d) 45 days
37. 37.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 13 days (c) 5 days (d) 21 days
38. 38.6 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 31 days (c) 12 days (d) 30 days
39. 39.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 20 days (c) 13 days (d) 7 days
40. 40.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 12 days (c) 9 days (d) 4 days

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