Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 403 · 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. 1.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 1 day (c) 3 days (d) 11 days
2. 2.If 5 notebooks cost ₹110, how much do 3 notebooks cost? (a) ₹108 (b) ₹66 (c) ₹330 (d) ₹88
3. 3.If 7 mangoes cost ₹161, how much do 11 mangoes cost? (a) ₹1771 (b) ₹165 (c) ₹253 (d) ₹276
4. 4.If 9 notebooks cost ₹207, how much do 10 notebooks cost? (a) ₹230 (b) ₹208 (c) ₹253 (d) ₹2070
5. 5.₹490 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹441 (b) ₹245 (c) ₹49 (d) ₹490
6. 6.If 6 notebooks cost ₹132, how much do 10 notebooks cost? (a) ₹136 (b) ₹1320 (c) ₹220 (d) ₹242
7. 7.If 2 pens cost ₹28, how much do 12 pens cost? (a) ₹38 (b) ₹336 (c) ₹182 (d) ₹168
8. 8.₹322 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹115 (b) ₹161 (c) ₹207 (d) ₹23
9. 9.₹120 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹15 (b) ₹60 (c) ₹45 (d) ₹75
10. 10.6 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) 16 days (d) 27 days
11. 11.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 11 days (c) 5 days (d) 14 days
12. 12.₹209 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹76 (b) ₹19 (c) ₹133 (d) ₹152
13. 13.If 4 kites cost ₹72, how much do 9 kites cost? (a) ₹180 (b) ₹77 (c) ₹648 (d) ₹162
14. 14.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 7 days (d) 2 days
15. 15.₹342 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹171 (b) ₹266 (c) ₹76 (d) ₹38
16. 16.If 2 kites cost ₹40, how much do 3 kites cost? (a) ₹60 (b) ₹120 (c) ₹80 (d) ₹41
17. 17.If 2 notebooks cost ₹8, how much do 10 notebooks cost? (a) ₹44 (b) ₹40 (c) ₹16 (d) ₹80
18. 18.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 1 day (d) 4 days
19. 19.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 12 days (d) 4 days
20. 20.If 2 notebooks cost ₹26, how much do 3 notebooks cost? (a) ₹27 (b) ₹78 (c) ₹52 (d) ₹39
21. 21.₹270 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹60 (b) ₹210 (c) ₹135 (d) ₹30
22. 22.₹184 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹92 (b) ₹184 (c) ₹161 (d) ₹23
23. 23.6 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 11 days (c) 7 days (d) 28 days
24. 24.₹44 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹33 (b) ₹11 (c) ₹22 (d) ₹44
25. 25.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 13 days (d) 12 days
26. 26.₹172 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹43 (b) ₹172 (c) ₹86 (d) ₹129
27. 27.₹440 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹220 (b) ₹40 (c) ₹160 (d) ₹280
28. 28.If 4 notebooks cost ₹84, how much do 5 notebooks cost? (a) ₹85 (b) ₹126 (c) ₹105 (d) ₹420
29. 29.3 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) 12 days (d) 3 days
30. 30.₹252 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹216 (b) ₹36 (c) ₹252 (d) ₹126
31. 31.₹144 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹64 (b) ₹16 (c) ₹72 (d) ₹80
32. 32.₹90 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹20 (b) ₹45 (c) ₹70 (d) ₹10
33. 33.If 4 notebooks cost ₹12, how much do 11 notebooks cost? (a) ₹36 (b) ₹33 (c) ₹19 (d) ₹132
34. 34.₹297 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹270 (b) ₹27 (c) ₹243 (d) ₹54
35. 35.If 8 notebooks cost ₹32, how much do 4 notebooks cost? (a) ₹16 (b) ₹128 (c) ₹28 (d) ₹20
36. 36.If 6 pens cost ₹144, how much do 11 pens cost? (a) ₹288 (b) ₹149 (c) ₹264 (d) ₹1584
37. 37.If 2 pens cost ₹44, how much do 3 pens cost? (a) ₹132 (b) ₹88 (c) ₹45 (d) ₹66
38. 38.₹340 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹306 (b) ₹340 (c) ₹170 (d) ₹34
39. 39.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 34 days (b) 7 days (c) 33 days (d) 15 days
40. 40.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 18 days (b) 5 days (c) 3 days (d) 4 days

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