Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 97 · 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 9 kites cost ₹162, how much do 3 kites cost? (a) ₹72 (b) ₹54 (c) ₹486 (d) ₹156
2. 2.If 2 pens cost ₹10, how much do 3 pens cost? (a) ₹11 (b) ₹15 (c) ₹30 (d) ₹20
3. 3.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 4 days (c) 3 days (d) 15 days
4. 4.If 7 pens cost ₹70, how much do 12 pens cost? (a) ₹840 (b) ₹120 (c) ₹130 (d) ₹75
5. 5.₹448 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹160 (b) ₹224 (c) ₹288 (d) ₹32
6. 6.6 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
7. 7.If 3 kites cost ₹51, how much do 10 kites cost? (a) ₹187 (b) ₹510 (c) ₹58 (d) ₹170
8. 8.If 4 mangoes cost ₹88, how much do 2 mangoes cost? (a) ₹176 (b) ₹44 (c) ₹86 (d) ₹66
9. 9.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 1 day (c) 22 days (d) 21 days
10. 10.8 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 8 days (d) 7 days
11. 11.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 13 days (d) 9 days
12. 12.₹220 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹44 (b) ₹220 (c) ₹110 (d) ₹176
13. 13.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 24 days (c) 10 days (d) 6 days
14. 14.₹204 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹34 (b) ₹204 (c) ₹170 (d) ₹102
15. 15.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 7 days (c) 19 days (d) 40 days
16. 16.If 9 kites cost ₹162, how much do 5 kites cost? (a) ₹90 (b) ₹158 (c) ₹810 (d) ₹108
17. 17.If 2 kites cost ₹40, how much do 9 kites cost? (a) ₹47 (b) ₹360 (c) ₹200 (d) ₹180
18. 18.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 3 days (d) 15 days
19. 19.₹364 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹112 (b) ₹252 (c) ₹28 (d) ₹182
20. 20.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 18 days (d) 14 days
21. 21.If 6 notebooks cost ₹66, how much do 7 notebooks cost? (a) ₹67 (b) ₹462 (c) ₹88 (d) ₹77
22. 22.If 4 pens cost ₹68, how much do 11 pens cost? (a) ₹748 (b) ₹204 (c) ₹187 (d) ₹75
23. 23.₹76 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹19 (b) ₹57 (c) ₹76 (d) ₹38
24. 24.If 9 kites cost ₹207, how much do 11 kites cost? (a) ₹209 (b) ₹2277 (c) ₹276 (d) ₹253
25. 25.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 22 days (c) 15 days (d) 23 days
26. 26.If 5 pens cost ₹90, how much do 10 pens cost? (a) ₹95 (b) ₹900 (c) ₹198 (d) ₹180
27. 27.₹112 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹32 (b) ₹80 (c) ₹16 (d) ₹56
28. 28.₹170 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹102 (b) ₹85 (c) ₹68 (d) ₹34
29. 29.If 3 notebooks cost ₹63, how much do 2 notebooks cost? (a) ₹42 (b) ₹63 (c) ₹62 (d) ₹126
30. 30.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 8 days (d) 9 days
31. 31.If 4 mangoes cost ₹44, how much do 12 mangoes cost? (a) ₹143 (b) ₹528 (c) ₹132 (d) ₹52
32. 32.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 15 days (b) 16 days (c) 13 days (d) 17 days
33. 33.₹539 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹98 (b) ₹441 (c) ₹49 (d) ₹490
34. 34.If 9 notebooks cost ₹153, how much do 10 notebooks cost? (a) ₹1530 (b) ₹170 (c) ₹187 (d) ₹154
35. 35.If 5 mangoes cost ₹75, how much do 9 mangoes cost? (a) ₹135 (b) ₹79 (c) ₹675 (d) ₹150
36. 36.6 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 12 days (c) 13 days (d) 15 days
37. 37.If 7 notebooks cost ₹70, how much do 10 notebooks cost? (a) ₹110 (b) ₹100 (c) ₹73 (d) ₹700
38. 38.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 7 days (d) 14 days
39. 39.₹286 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹26 (b) ₹156 (c) ₹130 (d) ₹143
40. 40.If 8 mangoes cost ₹152, how much do 10 mangoes cost? (a) ₹1520 (b) ₹209 (c) ₹190 (d) ₹154

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