Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 101 · 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. 1.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 19 days (c) 52 days (d) 53 days
2. 2.₹108 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹12 (b) ₹54 (c) ₹84 (d) ₹24
3. 3.₹40 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹5 (b) ₹20 (c) ₹15 (d) ₹25
4. 4.If 7 mangoes cost ₹105, how much do 10 mangoes cost? (a) ₹150 (b) ₹165 (c) ₹108 (d) ₹1050
5. 5.₹30 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹30 (b) ₹10 (c) ₹15 (d) ₹20
6. 6.6 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 10 days (d) 6 days
7. 7.If 3 mangoes cost ₹51, how much do 9 mangoes cost? (a) ₹170 (b) ₹459 (c) ₹57 (d) ₹153
8. 8.8 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 19 days (d) 11 days
9. 9.If 5 pens cost ₹125, how much do 8 pens cost? (a) ₹1000 (b) ₹128 (c) ₹225 (d) ₹200
10. 10.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 25 days (d) 9 days
11. 11.If 9 pens cost ₹81, how much do 10 pens cost? (a) ₹810 (b) ₹99 (c) ₹90 (d) ₹82
12. 12.If 4 mangoes cost ₹20, how much do 6 mangoes cost? (a) ₹120 (b) ₹35 (c) ₹30 (d) ₹22
13. 13.If 5 pens cost ₹100, how much do 2 pens cost? (a) ₹97 (b) ₹200 (c) ₹60 (d) ₹40
14. 14.If 2 kites cost ₹18, how much do 6 kites cost? (a) ₹63 (b) ₹108 (c) ₹54 (d) ₹22
15. 15.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 14 days (c) 18 days (d) 2 days
16. 16.If 5 pens cost ₹85, how much do 6 pens cost? (a) ₹510 (b) ₹119 (c) ₹102 (d) ₹86
17. 17.₹160 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹140 (b) ₹160 (c) ₹80 (d) ₹20
18. 18.If 2 kites cost ₹16, how much do 12 kites cost? (a) ₹192 (b) ₹26 (c) ₹96 (d) ₹104
19. 19.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 16 days (c) 11 days (d) 4 days
20. 20.8 workers can build a wall in 15 days. How many days will 4 workers take, working at the same speed? (a) 31 days (b) 30 days (c) 19 days (d) 11 days
21. 21.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 13 days (c) 5 days (d) 4 days
22. 22.If 6 mangoes cost ₹72, how much do 10 mangoes cost? (a) ₹720 (b) ₹120 (c) ₹76 (d) ₹132
23. 23.If 2 notebooks cost ₹44, how much do 11 notebooks cost? (a) ₹264 (b) ₹484 (c) ₹53 (d) ₹242
24. 24.If 5 pens cost ₹100, how much do 4 pens cost? (a) ₹80 (b) ₹400 (c) ₹100 (d) ₹99
25. 25.₹72 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹32 (b) ₹8 (c) ₹40 (d) ₹36
26. 26.₹130 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹39 (b) ₹13 (c) ₹65 (d) ₹91
27. 27.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 17 days (c) 4 days (d) 5 days
28. 28.₹273 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹210 (b) ₹21 (c) ₹84 (d) ₹189
29. 29.₹468 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹234 (b) ₹144 (c) ₹36 (d) ₹324
30. 30.If 9 notebooks cost ₹45, how much do 11 notebooks cost? (a) ₹47 (b) ₹55 (c) ₹60 (d) ₹495
31. 31.₹208 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹16 (b) ₹144 (c) ₹104 (d) ₹64
32. 32.₹484 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹44 (b) ₹242 (c) ₹352 (d) ₹132
33. 33.₹414 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹46 (b) ₹92 (c) ₹207 (d) ₹322
34. 34.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 27 days (b) 19 days (c) 28 days (d) 11 days
35. 35.If 5 notebooks cost ₹80, how much do 11 notebooks cost? (a) ₹176 (b) ₹880 (c) ₹86 (d) ₹192
36. 36.If 7 pens cost ₹91, how much do 8 pens cost? (a) ₹117 (b) ₹728 (c) ₹104 (d) ₹92
37. 37.₹66 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹66 (b) ₹33 (c) ₹11 (d) ₹55
38. 38.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 12 days (c) 6 days (d) 18 days
39. 39.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 13 days (c) 7 days (d) 25 days
40. 40.₹315 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹140 (b) ₹210 (c) ₹35 (d) ₹175

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