Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 831 · 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 12 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 7 days (c) 33 days (d) 32 days
2. 2.₹161 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹139 (b) ₹23 (c) ₹138 (d) ₹161
3. 3.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 1 day (d) 9 days
4. 4.₹363 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹231 (b) ₹165 (c) ₹33 (d) ₹198
5. 5.If 8 pens cost ₹96, how much do 11 pens cost? (a) ₹99 (b) ₹132 (c) ₹1056 (d) ₹144
6. 6.₹55 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹11 (b) ₹22 (c) ₹33 (d) ₹44
7. 7.If 4 mangoes cost ₹40, how much do 5 mangoes cost? (a) ₹50 (b) ₹200 (c) ₹60 (d) ₹41
8. 8.₹72 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹24 (b) ₹36 (c) ₹48 (d) ₹72
9. 9.₹324 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹36 (b) ₹144 (c) ₹162 (d) ₹180
10. 10.₹259 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹185 (b) ₹74 (c) ₹37 (d) ₹222
11. 11.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 4 days (d) 2 days
12. 12.₹352 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹128 (b) ₹32 (c) ₹224 (d) ₹176
13. 13.If 7 pens cost ₹168, how much do 5 pens cost? (a) ₹166 (b) ₹840 (c) ₹144 (d) ₹120
14. 14.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 4 days (d) 2 days
15. 15.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 24 days (c) 6 days (d) 15 days
16. 16.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 14 days (d) 15 days
17. 17.₹364 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹182 (b) ₹112 (c) ₹28 (d) ₹252
18. 18.If 7 pens cost ₹147, how much do 3 pens cost? (a) ₹63 (b) ₹143 (c) ₹84 (d) ₹441
19. 19.₹120 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹120 (b) ₹20 (c) ₹100 (d) ₹60
20. 20.₹473 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹86 (b) ₹387 (c) ₹430 (d) ₹43
21. 21.4 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) 14 days (d) 9 days
22. 22.₹30 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹15 (b) ₹12 (c) ₹6 (d) ₹18
23. 23.₹455 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹280 (b) ₹175 (c) ₹35 (d) ₹315
24. 24.If 3 pens cost ₹33, how much do 8 pens cost? (a) ₹264 (b) ₹88 (c) ₹38 (d) ₹99
25. 25.If 5 mangoes cost ₹90, how much do 11 mangoes cost? (a) ₹198 (b) ₹990 (c) ₹216 (d) ₹96
26. 26.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 18 days (b) 7 days (c) 10 days (d) 28 days
27. 27.₹248 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹248 (b) ₹124 (c) ₹31 (d) ₹217
28. 28.If 5 pens cost ₹60, how much do 4 pens cost? (a) ₹60 (b) ₹48 (c) ₹240 (d) ₹59
29. 29.8 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 60 days (b) 9 days (c) 61 days (d) 21 days
30. 30.If 6 kites cost ₹18, how much do 7 kites cost? (a) ₹126 (b) ₹19 (c) ₹24 (d) ₹21
31. 31.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 39 days (b) 17 days (c) 9 days (d) 40 days
32. 32.₹288 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹32 (b) ₹64 (c) ₹224 (d) ₹144
33. 33.If 6 pens cost ₹72, how much do 10 pens cost? (a) ₹120 (b) ₹720 (c) ₹76 (d) ₹132
34. 34.₹312 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹156 (b) ₹130 (c) ₹26 (d) ₹182
35. 35.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 7 days (c) 28 days (d) 12 days
36. 36.₹405 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹360 (b) ₹90 (c) ₹45 (d) ₹315
37. 37.₹78 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹6 (b) ₹24 (c) ₹39 (d) ₹54
38. 38.If 6 notebooks cost ₹114, how much do 11 notebooks cost? (a) ₹228 (b) ₹119 (c) ₹209 (d) ₹1254
39. 39.7 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 8 days (c) 28 days (d) 29 days
40. 40.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 20 days (b) 5 days (c) 6 days (d) 14 days

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