Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 367 · 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. 1.6 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 16 days (c) 22 days (d) 21 days
2. 2.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 21 days (c) 20 days (d) 19 days
3. 3.If 3 notebooks cost ₹21, how much do 4 notebooks cost? (a) ₹84 (b) ₹28 (c) ₹22 (d) ₹35
4. 4.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 8 days (d) 11 days
5. 5.3 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 16 days (d) 4 days
6. 6.If 4 kites cost ₹68, how much do 10 kites cost? (a) ₹187 (b) ₹680 (c) ₹74 (d) ₹170
7. 7.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 6 days (c) 8 days (d) 7 days
8. 8.₹91 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹70 (b) ₹63 (c) ₹7 (d) ₹28
9. 9.If 2 pens cost ₹48, how much do 3 pens cost? (a) ₹72 (b) ₹96 (c) ₹49 (d) ₹144
10. 10.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 15 days (b) 20 days (c) 5 days (d) 6 days
11. 11.If 2 mangoes cost ₹18, how much do 4 mangoes cost? (a) ₹72 (b) ₹45 (c) ₹36 (d) ₹20
12. 12.If 7 notebooks cost ₹77, how much do 8 notebooks cost? (a) ₹99 (b) ₹78 (c) ₹616 (d) ₹88
13. 13.If 4 pens cost ₹28, how much do 10 pens cost? (a) ₹77 (b) ₹280 (c) ₹70 (d) ₹34
14. 14.₹264 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹33 (b) ₹165 (c) ₹99 (d) ₹132
15. 15.₹143 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹117 (b) ₹13 (c) ₹39 (d) ₹104
16. 16.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 18 days (c) 11 days (d) 8 days
17. 17.₹126 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹126 (b) ₹18 (c) ₹63 (d) ₹108
18. 18.If 7 mangoes cost ₹63, how much do 8 mangoes cost? (a) ₹64 (b) ₹72 (c) ₹504 (d) ₹81
19. 19.₹650 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹400 (b) ₹325 (c) ₹250 (d) ₹50
20. 20.If 2 mangoes cost ₹8, how much do 9 mangoes cost? (a) ₹40 (b) ₹15 (c) ₹72 (d) ₹36
21. 21.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 5 days (c) 4 days (d) 11 days
22. 22.6 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 31 days (c) 12 days (d) 30 days
23. 23.₹400 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹50 (b) ₹150 (c) ₹200 (d) ₹250
24. 24.₹162 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹144 (b) ₹18 (c) ₹162 (d) ₹81
25. 25.₹215 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹173 (b) ₹43 (c) ₹172 (d) ₹215
26. 26.₹276 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹138 (b) ₹23 (c) ₹161 (d) ₹115
27. 27.If 3 pens cost ₹15, how much do 5 pens cost? (a) ₹25 (b) ₹75 (c) ₹30 (d) ₹17
28. 28.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 12 days (c) 4 days (d) 16 days
29. 29.₹552 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹46 (b) ₹322 (c) ₹276 (d) ₹230
30. 30.₹96 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹96 (b) ₹16 (c) ₹48 (d) ₹80
31. 31.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 20 days (b) 14 days (c) 16 days (d) 21 days
32. 32.₹340 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹340 (b) ₹34 (c) ₹306 (d) ₹170
33. 33.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 21 days (d) 17 days
34. 34.If 6 kites cost ₹60, how much do 8 kites cost? (a) ₹62 (b) ₹90 (c) ₹480 (d) ₹80
35. 35.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 26 days (b) 10 days (c) 27 days (d) 16 days
36. 36.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 6 days (d) 2 days
37. 37.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 22 days (c) 9 days (d) 13 days
38. 38.If 3 notebooks cost ₹15, how much do 9 notebooks cost? (a) ₹135 (b) ₹45 (c) ₹21 (d) ₹50
39. 39.4 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 14 days (d) 18 days
40. 40.If 2 pens cost ₹6, how much do 8 pens cost? (a) ₹48 (b) ₹24 (c) ₹27 (d) ₹12

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