Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 178 · 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 8 kites cost ₹64, how much do 9 kites cost? (a) ₹80 (b) ₹72 (c) ₹65 (d) ₹576
2. 2.If 4 kites cost ₹56, how much do 10 kites cost? (a) ₹560 (b) ₹140 (c) ₹62 (d) ₹154
3. 3.₹528 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹264 (b) ₹44 (c) ₹220 (d) ₹308
4. 4.₹208 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹64 (b) ₹104 (c) ₹144 (d) ₹16
5. 5.₹252 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹126 (b) ₹140 (c) ₹28 (d) ₹112
6. 6.₹384 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹192 (b) ₹160 (c) ₹32 (d) ₹224
7. 7.If 6 mangoes cost ₹66, how much do 2 mangoes cost? (a) ₹62 (b) ₹22 (c) ₹33 (d) ₹132
8. 8.If 3 mangoes cost ₹18, how much do 4 mangoes cost? (a) ₹24 (b) ₹30 (c) ₹19 (d) ₹72
9. 9.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 13 days
10. 10.₹217 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹217 (b) ₹187 (c) ₹186 (d) ₹31
11. 11.₹372 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹155 (b) ₹31 (c) ₹217 (d) ₹186
12. 12.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 26 days (d) 27 days
13. 13.₹176 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹22 (b) ₹154 (c) ₹88 (d) ₹176
14. 14.₹30 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹6 (b) ₹12 (c) ₹15 (d) ₹18
15. 15.If 4 mangoes cost ₹52, how much do 8 mangoes cost? (a) ₹117 (b) ₹416 (c) ₹104 (d) ₹56
16. 16.If 9 pens cost ₹216, how much do 12 pens cost? (a) ₹2592 (b) ₹219 (c) ₹288 (d) ₹312
17. 17.₹77 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹35 (b) ₹7 (c) ₹42 (d) ₹49
18. 18.If 6 notebooks cost ₹108, how much do 4 notebooks cost? (a) ₹72 (b) ₹90 (c) ₹432 (d) ₹106
19. 19.₹189 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹42 (b) ₹147 (c) ₹21 (d) ₹168
20. 20.If 3 mangoes cost ₹63, how much do 4 mangoes cost? (a) ₹105 (b) ₹252 (c) ₹64 (d) ₹84
21. 21.If 9 mangoes cost ₹171, how much do 7 mangoes cost? (a) ₹1197 (b) ₹152 (c) ₹169 (d) ₹133
22. 22.₹75 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹25 (b) ₹75 (c) ₹50 (d) ₹51
23. 23.If 2 pens cost ₹28, how much do 10 pens cost? (a) ₹280 (b) ₹36 (c) ₹154 (d) ₹140
24. 24.₹105 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹71 (b) ₹105 (c) ₹35 (d) ₹70
25. 25.₹24 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹18 (b) ₹24 (c) ₹6 (d) ₹12
26. 26.If 8 mangoes cost ₹48, how much do 4 mangoes cost? (a) ₹24 (b) ₹30 (c) ₹192 (d) ₹44
27. 27.If 2 pens cost ₹44, how much do 9 pens cost? (a) ₹396 (b) ₹198 (c) ₹220 (d) ₹51
28. 28.₹55 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹5 (b) ₹35 (c) ₹25 (d) ₹30
29. 29.₹492 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹41 (b) ₹205 (c) ₹246 (d) ₹287
30. 30.₹360 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹45 (b) ₹180 (c) ₹225 (d) ₹135
31. 31.₹176 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹48 (b) ₹128 (c) ₹16 (d) ₹88
32. 32.7 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) 49 days (d) 9 days
33. 33.5 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 19 days
34. 34.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 18 days (c) 19 days (d) 11 days
35. 35.₹64 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹48 (b) ₹32 (c) ₹64 (d) ₹16
36. 36.4 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 36 days (c) 20 days (d) 4 days
37. 37.₹80 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹10 (b) ₹40 (c) ₹70 (d) ₹80
38. 38.If 2 notebooks cost ₹10, how much do 3 notebooks cost? (a) ₹20 (b) ₹15 (c) ₹30 (d) ₹11
39. 39.If 5 kites cost ₹110, how much do 11 kites cost? (a) ₹264 (b) ₹1210 (c) ₹116 (d) ₹242
40. 40.₹360 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹210 (b) ₹150 (c) ₹30 (d) ₹180

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