Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 474 · 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.₹650 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹50 (b) ₹325 (c) ₹400 (d) ₹250
2. 2.If 9 notebooks cost ₹108, how much do 4 notebooks cost? (a) ₹60 (b) ₹432 (c) ₹48 (d) ₹103
3. 3.₹533 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹205 (b) ₹328 (c) ₹369 (d) ₹41
4. 4.If 5 mangoes cost ₹35, how much do 7 mangoes cost? (a) ₹37 (b) ₹56 (c) ₹245 (d) ₹49
5. 5.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 11 days (d) 1 day
6. 6.₹234 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹117 (b) ₹26 (c) ₹104 (d) ₹130
7. 7.If 2 mangoes cost ₹16, how much do 3 mangoes cost? (a) ₹48 (b) ₹24 (c) ₹32 (d) ₹17
8. 8.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 36 days (c) 17 days (d) 35 days
9. 9.₹91 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹91 (b) ₹79 (c) ₹78 (d) ₹13
10. 10.₹182 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹104 (b) ₹78 (c) ₹91 (d) ₹26
11. 11.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 12 days (b) 11 days (c) 3 days (d) 1 day
12. 12.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 5 days (d) 9 days
13. 13.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 3 days (d) 12 days
14. 14.If 7 mangoes cost ₹91, how much do 4 mangoes cost? (a) ₹52 (b) ₹364 (c) ₹88 (d) ₹65
15. 15.If 6 mangoes cost ₹60, how much do 7 mangoes cost? (a) ₹70 (b) ₹61 (c) ₹420 (d) ₹80
16. 16.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 16 days (c) 17 days (d) 10 days
17. 17.₹187 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹34 (b) ₹153 (c) ₹170 (d) ₹17
18. 18.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 14 days (b) 11 days (c) 15 days (d) 5 days
19. 19.₹77 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹67 (b) ₹11 (c) ₹77 (d) ₹66
20. 20.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 6 days (c) 18 days (d) 7 days
21. 21.If 6 kites cost ₹30, how much do 5 kites cost? (a) ₹29 (b) ₹150 (c) ₹30 (d) ₹25
22. 22.₹506 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹46 (b) ₹414 (c) ₹253 (d) ₹92
23. 23.If 2 kites cost ₹30, how much do 9 kites cost? (a) ₹150 (b) ₹270 (c) ₹135 (d) ₹37
24. 24.₹280 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹280 (b) ₹140 (c) ₹28 (d) ₹252
25. 25.If 7 kites cost ₹91, how much do 12 kites cost? (a) ₹96 (b) ₹156 (c) ₹1092 (d) ₹169
26. 26.If 2 pens cost ₹42, how much do 7 pens cost? (a) ₹47 (b) ₹147 (c) ₹168 (d) ₹294
27. 27.If 2 pens cost ₹46, how much do 10 pens cost? (a) ₹230 (b) ₹460 (c) ₹54 (d) ₹253
28. 28.If 8 notebooks cost ₹80, how much do 2 notebooks cost? (a) ₹30 (b) ₹20 (c) ₹160 (d) ₹74
29. 29.If 9 notebooks cost ₹126, how much do 2 notebooks cost? (a) ₹42 (b) ₹119 (c) ₹252 (d) ₹28
30. 30.If 2 notebooks cost ₹32, how much do 8 notebooks cost? (a) ₹38 (b) ₹128 (c) ₹144 (d) ₹256
31. 31.If 4 mangoes cost ₹88, how much do 8 mangoes cost? (a) ₹92 (b) ₹198 (c) ₹704 (d) ₹176
32. 32.If 8 kites cost ₹168, how much do 10 kites cost? (a) ₹231 (b) ₹210 (c) ₹170 (d) ₹1680
33. 33.If 4 pens cost ₹84, how much do 2 pens cost? (a) ₹168 (b) ₹42 (c) ₹82 (d) ₹63
34. 34.If 4 kites cost ₹28, how much do 5 kites cost? (a) ₹35 (b) ₹42 (c) ₹29 (d) ₹140
35. 35.If 6 pens cost ₹42, how much do 4 pens cost? (a) ₹28 (b) ₹40 (c) ₹168 (d) ₹35
36. 36.6 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 14 days (c) 10 days (d) 18 days
37. 37.If 8 pens cost ₹112, how much do 12 pens cost? (a) ₹182 (b) ₹168 (c) ₹116 (d) ₹1344
38. 38.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 16 days (c) 15 days (d) 9 days
39. 39.If 3 notebooks cost ₹33, how much do 6 notebooks cost? (a) ₹77 (b) ₹36 (c) ₹198 (d) ₹66
40. 40.If 4 pens cost ₹88, how much do 3 pens cost? (a) ₹66 (b) ₹87 (c) ₹264 (d) ₹88

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