Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 886 · 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 4 notebooks cost ₹60, how much do 9 notebooks cost? (a) ₹150 (b) ₹65 (c) ₹540 (d) ₹135
2. 2.₹390 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹240 (b) ₹195 (c) ₹150 (d) ₹30
3. 3.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 25 days (c) 13 days (d) 17 days
4. 4.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 20 days (b) 6 days (c) 5 days (d) 15 days
5. 5.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 49 days (b) 9 days (c) 4 days (d) 19 days
6. 6.If 2 notebooks cost ₹8, how much do 9 notebooks cost? (a) ₹36 (b) ₹40 (c) ₹72 (d) ₹15
7. 7.₹170 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹170 (b) ₹85 (c) ₹153 (d) ₹17
8. 8.If 9 kites cost ₹72, how much do 7 kites cost? (a) ₹64 (b) ₹70 (c) ₹56 (d) ₹504
9. 9.If 3 mangoes cost ₹39, how much do 7 mangoes cost? (a) ₹91 (b) ₹43 (c) ₹104 (d) ₹273
10. 10.₹180 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹144 (b) ₹36 (c) ₹180 (d) ₹90
11. 11.₹224 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹28 (b) ₹112 (c) ₹196 (d) ₹224
12. 12.If 4 pens cost ₹20, how much do 2 pens cost? (a) ₹40 (b) ₹18 (c) ₹15 (d) ₹10
13. 13.If 7 mangoes cost ₹126, how much do 9 mangoes cost? (a) ₹1134 (b) ₹128 (c) ₹162 (d) ₹180
14. 14.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 16 days (d) 17 days
15. 15.₹248 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹93 (b) ₹155 (c) ₹31 (d) ₹124
16. 16.₹88 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹8 (b) ₹24 (c) ₹64 (d) ₹44
17. 17.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 29 days (c) 13 days (d) 28 days
18. 18.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 4 days (d) 5 days
19. 19.If 3 notebooks cost ₹30, how much do 7 notebooks cost? (a) ₹34 (b) ₹210 (c) ₹80 (d) ₹70
20. 20.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 3 days (d) 28 days
21. 21.If 6 mangoes cost ₹24, how much do 12 mangoes cost? (a) ₹52 (b) ₹30 (c) ₹48 (d) ₹288
22. 22.₹528 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹264 (b) ₹192 (c) ₹336 (d) ₹48
23. 23.₹117 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹72 (b) ₹9 (c) ₹45 (d) ₹81
24. 24.If 8 mangoes cost ₹88, how much do 11 mangoes cost? (a) ₹132 (b) ₹121 (c) ₹91 (d) ₹968
25. 25.₹100 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹50 (b) ₹75 (c) ₹100 (d) ₹25
26. 26.If 6 pens cost ₹114, how much do 10 pens cost? (a) ₹209 (b) ₹1140 (c) ₹118 (d) ₹190
27. 27.9 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) 40 days (d) 19 days
28. 28.4 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 16 days (b) 13 days (c) 14 days (d) 12 days
29. 29.If 8 kites cost ₹48, how much do 5 kites cost? (a) ₹36 (b) ₹30 (c) ₹240 (d) ₹45
30. 30.If 4 notebooks cost ₹12, how much do 6 notebooks cost? (a) ₹14 (b) ₹21 (c) ₹18 (d) ₹72
31. 31.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 3 days (d) 8 days
32. 32.If 6 kites cost ₹48, how much do 3 kites cost? (a) ₹45 (b) ₹24 (c) ₹144 (d) ₹32
33. 33.If 2 pens cost ₹12, how much do 3 pens cost? (a) ₹36 (b) ₹18 (c) ₹13 (d) ₹24
34. 34.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 13 days
35. 35.If 7 kites cost ₹105, how much do 3 kites cost? (a) ₹60 (b) ₹315 (c) ₹101 (d) ₹45
36. 36.₹182 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹91 (b) ₹104 (c) ₹78 (d) ₹26
37. 37.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 27 days (c) 28 days (d) 13 days
38. 38.If 2 pens cost ₹28, how much do 4 pens cost? (a) ₹70 (b) ₹30 (c) ₹56 (d) ₹112
39. 39.If 2 pens cost ₹26, how much do 7 pens cost? (a) ₹31 (b) ₹104 (c) ₹182 (d) ₹91
40. 40.If 2 kites cost ₹18, how much do 4 kites cost? (a) ₹36 (b) ₹20 (c) ₹45 (d) ₹72

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