Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 728 · 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 4 kites cost ₹84, how much do 9 kites cost? (a) ₹189 (b) ₹756 (c) ₹210 (d) ₹89
2. 2.₹507 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹351 (b) ₹195 (c) ₹39 (d) ₹312
3. 3.₹188 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹47 (b) ₹141 (c) ₹188 (d) ₹94
4. 4.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 28 days (b) 7 days (c) 10 days (d) 18 days
5. 5.If 4 kites cost ₹28, how much do 7 kites cost? (a) ₹196 (b) ₹31 (c) ₹56 (d) ₹49
6. 6.₹75 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹30 (b) ₹45 (c) ₹15 (d) ₹60
7. 7.₹190 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹95 (b) ₹133 (c) ₹19 (d) ₹57
8. 8.6 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 22 days (c) 21 days (d) 16 days
9. 9.₹440 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹280 (b) ₹160 (c) ₹40 (d) ₹220
10. 10.If 6 pens cost ₹36, how much do 8 pens cost? (a) ₹288 (b) ₹54 (c) ₹48 (d) ₹38
11. 11.6 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 13 days (b) 11 days (c) 12 days (d) 15 days
12. 12.4 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 16 days (d) 11 days
13. 13.If 3 kites cost ₹51, how much do 11 kites cost? (a) ₹59 (b) ₹204 (c) ₹561 (d) ₹187
14. 14.₹132 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹132 (b) ₹22 (c) ₹66 (d) ₹110
15. 15.If 6 mangoes cost ₹150, how much do 7 mangoes cost? (a) ₹175 (b) ₹200 (c) ₹1050 (d) ₹151
16. 16.If 4 pens cost ₹16, how much do 9 pens cost? (a) ₹21 (b) ₹40 (c) ₹36 (d) ₹144
17. 17.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 28 days (d) 7 days
18. 18.If 9 kites cost ₹225, how much do 4 kites cost? (a) ₹900 (b) ₹220 (c) ₹125 (d) ₹100
19. 19.If 6 kites cost ₹18, how much do 5 kites cost? (a) ₹17 (b) ₹18 (c) ₹90 (d) ₹15
20. 20.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 43 days (c) 20 days (d) 42 days
21. 21.₹600 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹250 (b) ₹50 (c) ₹300 (d) ₹350
22. 22.If 2 mangoes cost ₹46, how much do 4 mangoes cost? (a) ₹115 (b) ₹184 (c) ₹92 (d) ₹48
23. 23.If 6 pens cost ₹114, how much do 8 pens cost? (a) ₹152 (b) ₹116 (c) ₹171 (d) ₹912
24. 24.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 4 days (c) 5 days (d) 6 days
25. 25.₹312 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹120 (b) ₹156 (c) ₹192 (d) ₹24
26. 26.If 5 pens cost ₹110, how much do 2 pens cost? (a) ₹220 (b) ₹66 (c) ₹107 (d) ₹44
27. 27.If 6 pens cost ₹144, how much do 7 pens cost? (a) ₹168 (b) ₹1008 (c) ₹145 (d) ₹192
28. 28.If 8 pens cost ₹168, how much do 6 pens cost? (a) ₹126 (b) ₹166 (c) ₹1008 (d) ₹147
29. 29.₹35 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹25 (b) ₹5 (c) ₹15 (d) ₹20
30. 30.If 2 notebooks cost ₹20, how much do 4 notebooks cost? (a) ₹40 (b) ₹50 (c) ₹80 (d) ₹22
31. 31.If 6 kites cost ₹144, how much do 7 kites cost? (a) ₹1008 (b) ₹145 (c) ₹168 (d) ₹192
32. 32.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 16 days (d) 5 days
33. 33.If 7 notebooks cost ₹133, how much do 4 notebooks cost? (a) ₹95 (b) ₹130 (c) ₹532 (d) ₹76
34. 34.4 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) 9 days (d) 14 days
35. 35.6 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 9 days (c) 11 days (d) 13 days
36. 36.8 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 10 days (d) 19 days
37. 37.If 9 kites cost ₹126, how much do 11 kites cost? (a) ₹1386 (b) ₹128 (c) ₹154 (d) ₹168
38. 38.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 16 days (c) 12 days (d) 4 days
39. 39.If 4 pens cost ₹32, how much do 2 pens cost? (a) ₹16 (b) ₹24 (c) ₹30 (d) ₹64
40. 40.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 5 days (d) 20 days

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