Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 876 · 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.₹192 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹24 (b) ₹72 (c) ₹96 (d) ₹120
2. 2.If 3 pens cost ₹12, how much do 12 pens cost? (a) ₹21 (b) ₹48 (c) ₹144 (d) ₹52
3. 3.6 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 16 days (d) 14 days
4. 4.If 5 mangoes cost ₹55, how much do 6 mangoes cost? (a) ₹56 (b) ₹77 (c) ₹330 (d) ₹66
5. 5.₹189 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹42 (b) ₹168 (c) ₹147 (d) ₹21
6. 6.6 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 7 days (c) 20 days (d) 5 days
7. 7.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 13 days (c) 26 days (d) 28 days
8. 8.If 2 notebooks cost ₹12, how much do 12 notebooks cost? (a) ₹78 (b) ₹72 (c) ₹22 (d) ₹144
9. 9.₹312 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹120 (b) ₹24 (c) ₹192 (d) ₹156
10. 10.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 1 day (c) 17 days (d) 10 days
11. 11.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 10 days (d) 11 days
12. 12.If 2 kites cost ₹30, how much do 4 kites cost? (a) ₹75 (b) ₹60 (c) ₹32 (d) ₹120
13. 13.If 8 pens cost ₹160, how much do 12 pens cost? (a) ₹164 (b) ₹1920 (c) ₹240 (d) ₹260
14. 14.₹341 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹279 (b) ₹248 (c) ₹93 (d) ₹31
15. 15.If 9 mangoes cost ₹99, how much do 12 mangoes cost? (a) ₹132 (b) ₹1188 (c) ₹102 (d) ₹143
16. 16.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 9 days (c) 4 days (d) 49 days
17. 17.If 3 pens cost ₹45, how much do 10 pens cost? (a) ₹165 (b) ₹52 (c) ₹150 (d) ₹450
18. 18.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 4 days (d) 6 days
19. 19.₹329 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹282 (b) ₹235 (c) ₹47 (d) ₹94
20. 20.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 14 days (c) 3 days (d) 15 days
21. 21.If 2 kites cost ₹50, how much do 7 kites cost? (a) ₹200 (b) ₹350 (c) ₹55 (d) ₹175
22. 22.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 15 days (c) 9 days (d) 14 days
23. 23.₹168 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹96 (b) ₹84 (c) ₹24 (d) ₹72
24. 24.₹93 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹62 (b) ₹93 (c) ₹63 (d) ₹31
25. 25.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 17 days (b) 28 days (c) 11 days (d) 7 days
26. 26.₹260 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹26 (b) ₹182 (c) ₹130 (d) ₹78
27. 27.If 8 pens cost ₹184, how much do 12 pens cost? (a) ₹188 (b) ₹299 (c) ₹276 (d) ₹2208
28. 28.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 10 days (c) 6 days (d) 24 days
29. 29.₹165 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹105 (b) ₹15 (c) ₹75 (d) ₹90
30. 30.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 34 days (d) 33 days
31. 31.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 21 days (c) 11 days (d) 20 days
32. 32.₹30 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹18 (b) ₹12 (c) ₹6 (d) ₹15
33. 33.If 2 kites cost ₹16, how much do 3 kites cost? (a) ₹24 (b) ₹17 (c) ₹32 (d) ₹48
34. 34.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 17 days (c) 11 days (d) 9 days
35. 35.₹42 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹12 (b) ₹21 (c) ₹6 (d) ₹30
36. 36.₹336 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹168 (b) ₹126 (c) ₹210 (d) ₹42
37. 37.If 2 mangoes cost ₹28, how much do 9 mangoes cost? (a) ₹126 (b) ₹252 (c) ₹140 (d) ₹35
38. 38.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 11 days (c) 15 days (d) 16 days
39. 39.If 7 kites cost ₹175, how much do 4 kites cost? (a) ₹172 (b) ₹700 (c) ₹125 (d) ₹100
40. 40.If 3 kites cost ₹51, how much do 5 kites cost? (a) ₹85 (b) ₹255 (c) ₹53 (d) ₹102

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