Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 514 · 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.If 5 pens cost ₹95, how much do 2 pens cost? (a) ₹92 (b) ₹190 (c) ₹38 (d) ₹57
2. 2.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 9 days (d) 49 days
3. 3.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 11 days (c) 9 days (d) 10 days
4. 4.₹385 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹280 (b) ₹140 (c) ₹245 (d) ₹35
5. 5.₹98 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹49 (b) ₹14 (c) ₹98 (d) ₹84
6. 6.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 5 days (d) 6 days
7. 7.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 5 days (d) 13 days
8. 8.₹396 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹288 (b) ₹198 (c) ₹108 (d) ₹36
9. 9.₹400 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹40 (b) ₹400 (c) ₹360 (d) ₹200
10. 10.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 27 days (c) 15 days (d) 26 days
11. 11.If 8 mangoes cost ₹152, how much do 9 mangoes cost? (a) ₹1368 (b) ₹190 (c) ₹171 (d) ₹153
12. 12.₹180 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹90 (b) ₹105 (c) ₹15 (d) ₹75
13. 13.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 7 days (d) 6 days
14. 14.If 3 mangoes cost ₹72, how much do 8 mangoes cost? (a) ₹216 (b) ₹576 (c) ₹192 (d) ₹77
15. 15.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 2 days (c) 16 days (d) 13 days
16. 16.If 7 pens cost ₹133, how much do 2 pens cost? (a) ₹38 (b) ₹57 (c) ₹128 (d) ₹266
17. 17.If 8 mangoes cost ₹104, how much do 2 mangoes cost? (a) ₹39 (b) ₹98 (c) ₹26 (d) ₹208
18. 18.If 8 mangoes cost ₹184, how much do 11 mangoes cost? (a) ₹2024 (b) ₹276 (c) ₹187 (d) ₹253
19. 19.₹250 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹100 (b) ₹150 (c) ₹125 (d) ₹50
20. 20.If 5 notebooks cost ₹30, how much do 2 notebooks cost? (a) ₹12 (b) ₹60 (c) ₹18 (d) ₹27
21. 21.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 12 days (c) 7 days (d) 16 days
22. 22.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 7 days (d) 4 days
23. 23.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 24 days (d) 16 days
24. 24.₹210 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹168 (b) ₹105 (c) ₹42 (d) ₹210
25. 25.If 3 pens cost ₹54, how much do 9 pens cost? (a) ₹180 (b) ₹486 (c) ₹162 (d) ₹60
26. 26.₹312 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹120 (b) ₹156 (c) ₹24 (d) ₹192
27. 27.₹130 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹65 (b) ₹52 (c) ₹78 (d) ₹26
28. 28.If 4 kites cost ₹52, how much do 5 kites cost? (a) ₹65 (b) ₹78 (c) ₹260 (d) ₹53
29. 29.If 4 pens cost ₹24, how much do 8 pens cost? (a) ₹28 (b) ₹192 (c) ₹54 (d) ₹48
30. 30.₹300 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹300 (b) ₹150 (c) ₹30 (d) ₹270
31. 31.If 3 notebooks cost ₹54, how much do 4 notebooks cost? (a) ₹216 (b) ₹55 (c) ₹90 (d) ₹72
32. 32.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 13 days (c) 11 days (d) 8 days
33. 33.₹108 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹90 (b) ₹108 (c) ₹18 (d) ₹54
34. 34.If 5 pens cost ₹30, how much do 12 pens cost? (a) ₹37 (b) ₹360 (c) ₹78 (d) ₹72
35. 35.₹220 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹20 (b) ₹140 (c) ₹110 (d) ₹80
36. 36.If 3 pens cost ₹18, how much do 8 pens cost? (a) ₹48 (b) ₹23 (c) ₹54 (d) ₹144
37. 37.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 19 days (c) 39 days (d) 7 days
38. 38.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 6 days (c) 7 days (d) 8 days
39. 39.₹616 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹220 (b) ₹44 (c) ₹308 (d) ₹396
40. 40.If 7 pens cost ₹21, how much do 3 pens cost? (a) ₹63 (b) ₹17 (c) ₹9 (d) ₹12

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