Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 751 · 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 mangoes cost ₹36, how much do 10 mangoes cost? (a) ₹360 (b) ₹42 (c) ₹99 (d) ₹90
2. 2.₹88 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹11 (b) ₹44 (c) ₹33 (d) ₹55
3. 3.₹247 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹76 (b) ₹19 (c) ₹190 (d) ₹171
4. 4.₹650 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹325 (b) ₹400 (c) ₹250 (d) ₹50
5. 5.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 18 days (c) 12 days (d) 19 days
6. 6.₹416 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹160 (b) ₹208 (c) ₹256 (d) ₹32
7. 7.₹68 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹17 (b) ₹68 (c) ₹51 (d) ₹34
8. 8.₹408 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹204 (b) ₹170 (c) ₹238 (d) ₹34
9. 9.If 9 pens cost ₹63, how much do 5 pens cost? (a) ₹59 (b) ₹315 (c) ₹35 (d) ₹42
10. 10.₹370 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹111 (b) ₹185 (c) ₹259 (d) ₹37
11. 11.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 18 days (b) 5 days (c) 4 days (d) 3 days
12. 12.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 12 days (b) 16 days (c) 4 days (d) 5 days
13. 13.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 21 days (b) 45 days (c) 9 days (d) 5 days
14. 14.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 21 days (d) 22 days
15. 15.If 3 notebooks cost ₹63, how much do 2 notebooks cost? (a) ₹63 (b) ₹42 (c) ₹126 (d) ₹62
16. 16.If 6 notebooks cost ₹144, how much do 4 notebooks cost? (a) ₹120 (b) ₹96 (c) ₹142 (d) ₹576
17. 17.If 9 kites cost ₹27, how much do 2 kites cost? (a) ₹54 (b) ₹6 (c) ₹9 (d) ₹20
18. 18.7 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 21 days (b) 9 days (c) 22 days (d) 15 days
19. 19.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 2 days (c) 19 days (d) 18 days
20. 20.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 29 days (c) 28 days (d) 13 days
21. 21.If 6 notebooks cost ₹144, how much do 12 notebooks cost? (a) ₹312 (b) ₹288 (c) ₹150 (d) ₹1728
22. 22.5 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 11 days (d) 9 days
23. 23.₹140 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹70 (b) ₹42 (c) ₹14 (d) ₹98
24. 24.If 5 kites cost ₹40, how much do 4 kites cost? (a) ₹40 (b) ₹32 (c) ₹39 (d) ₹160
25. 25.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 3 days (d) 10 days
26. 26.₹45 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹25 (b) ₹20 (c) ₹5 (d) ₹30
27. 27.₹242 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹22 (b) ₹110 (c) ₹132 (d) ₹121
28. 28.₹77 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹55 (b) ₹11 (c) ₹66 (d) ₹22
29. 29.₹66 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹6 (b) ₹33 (c) ₹30 (d) ₹36
30. 30.₹150 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹150 (b) ₹100 (c) ₹75 (d) ₹50
31. 31.If 8 mangoes cost ₹24, how much do 4 mangoes cost? (a) ₹96 (b) ₹15 (c) ₹12 (d) ₹20
32. 32.If 5 notebooks cost ₹35, how much do 3 notebooks cost? (a) ₹21 (b) ₹28 (c) ₹33 (d) ₹105
33. 33.₹119 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹34 (b) ₹85 (c) ₹17 (d) ₹102
34. 34.If 7 notebooks cost ₹28, how much do 11 notebooks cost? (a) ₹44 (b) ₹32 (c) ₹308 (d) ₹48
35. 35.If 6 notebooks cost ₹78, how much do 5 notebooks cost? (a) ₹77 (b) ₹65 (c) ₹390 (d) ₹78
36. 36.If 2 pens cost ₹32, how much do 12 pens cost? (a) ₹208 (b) ₹192 (c) ₹384 (d) ₹42
37. 37.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 7 days (d) 11 days
38. 38.If 4 pens cost ₹64, how much do 12 pens cost? (a) ₹192 (b) ₹768 (c) ₹208 (d) ₹72
39. 39.₹150 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹150 (b) ₹15 (c) ₹75 (d) ₹135
40. 40.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 28 days (c) 27 days (d) 13 days

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