Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 857 · 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 10 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 20 days (c) 7 days (d) 13 days
2. 2.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 21 days (c) 9 days (d) 45 days
3. 3.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 3 days (c) 4 days (d) 5 days
4. 4.₹110 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹66 (b) ₹22 (c) ₹44 (d) ₹55
5. 5.₹198 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹36 (b) ₹162 (c) ₹18 (d) ₹99
6. 6.If 9 kites cost ₹225, how much do 6 kites cost? (a) ₹150 (b) ₹175 (c) ₹222 (d) ₹1350
7. 7.If 7 kites cost ₹154, how much do 10 kites cost? (a) ₹157 (b) ₹1540 (c) ₹220 (d) ₹242
8. 8.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 31 days (d) 30 days
9. 9.If 3 kites cost ₹36, how much do 10 kites cost? (a) ₹360 (b) ₹132 (c) ₹120 (d) ₹43
10. 10.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 4 days (c) 14 days (d) 10 days
11. 11.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 18 days (b) 7 days (c) 6 days (d) 10 days
12. 12.If 7 kites cost ₹126, how much do 8 kites cost? (a) ₹127 (b) ₹144 (c) ₹1008 (d) ₹162
13. 13.8 workers can build a wall in 15 days. How many days will 4 workers take, working at the same speed? (a) 30 days (b) 11 days (c) 19 days (d) 31 days
14. 14.If 5 notebooks cost ₹30, how much do 4 notebooks cost? (a) ₹29 (b) ₹120 (c) ₹24 (d) ₹30
15. 15.If 6 kites cost ₹126, how much do 5 kites cost? (a) ₹105 (b) ₹630 (c) ₹126 (d) ₹125
16. 16.If 5 notebooks cost ₹25, how much do 6 notebooks cost? (a) ₹35 (b) ₹30 (c) ₹150 (d) ₹26
17. 17.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 12 days (b) 9 days (c) 3 days (d) 4 days
18. 18.₹136 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹136 (b) ₹17 (c) ₹68 (d) ₹119
19. 19.₹287 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹246 (b) ₹41 (c) ₹82 (d) ₹205
20. 20.₹126 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹126 (b) ₹112 (c) ₹63 (d) ₹14
21. 21.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 23 days (b) 22 days (c) 15 days (d) 7 days
22. 22.₹297 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹243 (b) ₹27 (c) ₹54 (d) ₹270
23. 23.₹48 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹24 (b) ₹18 (c) ₹30 (d) ₹6
24. 24.If 8 pens cost ₹48, how much do 10 pens cost? (a) ₹60 (b) ₹480 (c) ₹66 (d) ₹50
25. 25.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 25 days (c) 17 days (d) 13 days
26. 26.If 5 mangoes cost ₹115, how much do 9 mangoes cost? (a) ₹1035 (b) ₹230 (c) ₹119 (d) ₹207
27. 27.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 1 day (b) 9 days (c) 10 days (d) 8 days
28. 28.If 5 kites cost ₹115, how much do 6 kites cost? (a) ₹161 (b) ₹690 (c) ₹138 (d) ₹116
29. 29.If 4 mangoes cost ₹32, how much do 3 mangoes cost? (a) ₹31 (b) ₹96 (c) ₹32 (d) ₹24
30. 30.If 6 notebooks cost ₹72, how much do 3 notebooks cost? (a) ₹36 (b) ₹48 (c) ₹216 (d) ₹69
31. 31.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 2 days (d) 4 days
32. 32.₹186 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹31 (b) ₹186 (c) ₹93 (d) ₹155
33. 33.If 3 pens cost ₹66, how much do 8 pens cost? (a) ₹176 (b) ₹198 (c) ₹528 (d) ₹71
34. 34.If 6 notebooks cost ₹84, how much do 10 notebooks cost? (a) ₹154 (b) ₹840 (c) ₹140 (d) ₹88
35. 35.If 9 pens cost ₹54, how much do 11 pens cost? (a) ₹66 (b) ₹72 (c) ₹594 (d) ₹56
36. 36.If 3 mangoes cost ₹57, how much do 6 mangoes cost? (a) ₹114 (b) ₹133 (c) ₹342 (d) ₹60
37. 37.If 5 pens cost ₹85, how much do 3 pens cost? (a) ₹68 (b) ₹255 (c) ₹83 (d) ₹51
38. 38.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 11 days (d) 2 days
39. 39.₹216 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹180 (b) ₹216 (c) ₹108 (d) ₹36
40. 40.If 4 pens cost ₹96, how much do 7 pens cost? (a) ₹192 (b) ₹99 (c) ₹168 (d) ₹672

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