Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 268 · 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. 1.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 1 day
2. 2.₹344 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹43 (b) ₹301 (c) ₹172 (d) ₹344
3. 3.If 4 pens cost ₹32, how much do 5 pens cost? (a) ₹48 (b) ₹40 (c) ₹33 (d) ₹160
4. 4.If 2 notebooks cost ₹50, how much do 11 notebooks cost? (a) ₹300 (b) ₹550 (c) ₹59 (d) ₹275
5. 5.If 9 pens cost ₹153, how much do 11 pens cost? (a) ₹204 (b) ₹187 (c) ₹1683 (d) ₹155
6. 6.₹55 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹11 (b) ₹45 (c) ₹55 (d) ₹44
7. 7.If 6 kites cost ₹90, how much do 8 kites cost? (a) ₹120 (b) ₹92 (c) ₹720 (d) ₹135
8. 8.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 22 days (c) 21 days (d) 13 days
9. 9.If 6 kites cost ₹108, how much do 7 kites cost? (a) ₹144 (b) ₹756 (c) ₹109 (d) ₹126
10. 10.If 2 notebooks cost ₹28, how much do 10 notebooks cost? (a) ₹36 (b) ₹280 (c) ₹154 (d) ₹140
11. 11.₹55 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹45 (b) ₹15 (c) ₹5 (d) ₹40
12. 12.₹476 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹170 (b) ₹306 (c) ₹238 (d) ₹34
13. 13.If 6 pens cost ₹120, how much do 7 pens cost? (a) ₹840 (b) ₹140 (c) ₹121 (d) ₹160
14. 14.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 3 days (c) 2 days (d) 12 days
15. 15.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 15 days
16. 16.8 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 61 days (d) 60 days
17. 17.₹290 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹145 (b) ₹29 (c) ₹261 (d) ₹290
18. 18.₹473 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹344 (b) ₹43 (c) ₹387 (d) ₹129
19. 19.₹240 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹240 (b) ₹120 (c) ₹216 (d) ₹24
20. 20.₹456 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹38 (b) ₹228 (c) ₹190 (d) ₹266
21. 21.₹203 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹29 (b) ₹58 (c) ₹174 (d) ₹145
22. 22.₹126 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹14 (b) ₹63 (c) ₹56 (d) ₹70
23. 23.₹144 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹144 (b) ₹128 (c) ₹72 (d) ₹16
24. 24.₹200 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹20 (b) ₹100 (c) ₹200 (d) ₹180
25. 25.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 11 days
26. 26.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 36 days (d) 18 days
27. 27.₹52 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹26 (b) ₹39 (c) ₹52 (d) ₹13
28. 28.₹440 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹132 (b) ₹220 (c) ₹44 (d) ₹308
29. 29.If 7 kites cost ₹63, how much do 2 kites cost? (a) ₹18 (b) ₹58 (c) ₹126 (d) ₹27
30. 30.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 4 days (d) 9 days
31. 31.₹455 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹280 (b) ₹35 (c) ₹175 (d) ₹315
32. 32.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 31 days (b) 30 days (c) 17 days (d) 13 days
33. 33.If 5 notebooks cost ₹60, how much do 8 notebooks cost? (a) ₹96 (b) ₹63 (c) ₹480 (d) ₹108
34. 34.If 9 pens cost ₹207, how much do 4 pens cost? (a) ₹115 (b) ₹92 (c) ₹202 (d) ₹828
35. 35.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 3 days (d) 15 days
36. 36.If 3 kites cost ₹15, how much do 5 kites cost? (a) ₹75 (b) ₹30 (c) ₹25 (d) ₹17
37. 37.₹48 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹24 (b) ₹30 (c) ₹6 (d) ₹18
38. 38.₹312 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹182 (b) ₹156 (c) ₹130 (d) ₹26
39. 39.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 25 days (c) 24 days (d) 23 days
40. 40.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 11 days (c) 16 days (d) 17 days

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