Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 252 · 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 notebooks cost ₹22, how much do 10 notebooks cost? (a) ₹121 (b) ₹110 (c) ₹30 (d) ₹220
2. 2.If 2 kites cost ₹18, how much do 3 kites cost? (a) ₹36 (b) ₹19 (c) ₹54 (d) ₹27
3. 3.₹256 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹128 (b) ₹96 (c) ₹32 (d) ₹160
4. 4.If 3 kites cost ₹36, how much do 4 kites cost? (a) ₹60 (b) ₹37 (c) ₹144 (d) ₹48
5. 5.If 4 kites cost ₹16, how much do 11 kites cost? (a) ₹176 (b) ₹23 (c) ₹44 (d) ₹48
6. 6.If 4 mangoes cost ₹16, how much do 7 mangoes cost? (a) ₹32 (b) ₹28 (c) ₹19 (d) ₹112
7. 7.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 10 days (d) 5 days
8. 8.₹235 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹235 (b) ₹189 (c) ₹188 (d) ₹47
9. 9.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 26 days (b) 27 days (c) 10 days (d) 16 days
10. 10.If 9 notebooks cost ₹225, how much do 2 notebooks cost? (a) ₹450 (b) ₹75 (c) ₹218 (d) ₹50
11. 11.₹120 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹24 (b) ₹60 (c) ₹96 (d) ₹120
12. 12.If 3 kites cost ₹54, how much do 12 kites cost? (a) ₹234 (b) ₹63 (c) ₹648 (d) ₹216
13. 13.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 2 days (c) 3 days (d) 12 days
14. 14.If 9 kites cost ₹216, how much do 8 kites cost? (a) ₹1728 (b) ₹215 (c) ₹216 (d) ₹192
15. 15.If 2 notebooks cost ₹10, how much do 9 notebooks cost? (a) ₹17 (b) ₹45 (c) ₹50 (d) ₹90
16. 16.₹87 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹29 (b) ₹87 (c) ₹59 (d) ₹58
17. 17.If 9 mangoes cost ₹225, how much do 8 mangoes cost? (a) ₹200 (b) ₹225 (c) ₹224 (d) ₹1800
18. 18.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 10 days (d) 9 days
19. 19.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 13 days (d) 7 days
20. 20.If 7 mangoes cost ₹119, how much do 10 mangoes cost? (a) ₹187 (b) ₹122 (c) ₹1190 (d) ₹170
21. 21.If 2 pens cost ₹30, how much do 6 pens cost? (a) ₹180 (b) ₹34 (c) ₹90 (d) ₹105
22. 22.7 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) 21 days (d) 5 days
23. 23.If 2 kites cost ₹38, how much do 9 kites cost? (a) ₹190 (b) ₹45 (c) ₹342 (d) ₹171
24. 24.₹72 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹27 (b) ₹36 (c) ₹9 (d) ₹45
25. 25.₹40 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹30 (b) ₹20 (c) ₹40 (d) ₹10
26. 26.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 9 days (d) 15 days
27. 27.₹192 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹96 (b) ₹192 (c) ₹48 (d) ₹144
28. 28.₹111 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹37 (b) ₹111 (c) ₹74 (d) ₹75
29. 29.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 20 days (c) 14 days (d) 5 days
30. 30.If 7 mangoes cost ₹91, how much do 8 mangoes cost? (a) ₹92 (b) ₹104 (c) ₹728 (d) ₹117
31. 31.₹180 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹18 (b) ₹90 (c) ₹180 (d) ₹162
32. 32.₹429 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹297 (b) ₹33 (c) ₹165 (d) ₹264
33. 33.₹264 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹168 (b) ₹24 (c) ₹132 (d) ₹96
34. 34.9 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 7 days (d) 17 days
35. 35.₹455 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹35 (b) ₹315 (c) ₹140 (d) ₹350
36. 36.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹35 (b) ₹7 (c) ₹56 (d) ₹63
37. 37.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 28 days (c) 15 days (d) 3 days
38. 38.6 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 24 days (d) 18 days
39. 39.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 1 day (c) 9 days (d) 16 days
40. 40.₹462 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹231 (b) ₹252 (c) ₹210 (d) ₹42

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