Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 319 · 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 3 mangoes cost ₹36, how much do 9 mangoes cost? (a) ₹108 (b) ₹42 (c) ₹324 (d) ₹120
2. 2.₹294 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹252 (b) ₹294 (c) ₹147 (d) ₹42
3. 3.₹315 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹45 (b) ₹270 (c) ₹271 (d) ₹315
4. 4.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 16 days (d) 12 days
5. 5.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 15 days
6. 6.If 2 pens cost ₹28, how much do 12 pens cost? (a) ₹168 (b) ₹336 (c) ₹38 (d) ₹182
7. 7.If 5 mangoes cost ₹85, how much do 2 mangoes cost? (a) ₹51 (b) ₹34 (c) ₹170 (d) ₹82
8. 8.If 9 kites cost ₹54, how much do 8 kites cost? (a) ₹48 (b) ₹54 (c) ₹432 (d) ₹53
9. 9.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 16 days (d) 11 days
10. 10.₹65 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹53 (b) ₹52 (c) ₹13 (d) ₹65
11. 11.6 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 30 days (c) 31 days (d) 12 days
12. 12.6 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) 18 days (d) 10 days
13. 13.₹72 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹36 (b) ₹45 (c) ₹9 (d) ₹27
14. 14.₹242 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹44 (b) ₹198 (c) ₹22 (d) ₹121
15. 15.If 9 notebooks cost ₹27, how much do 7 notebooks cost? (a) ₹24 (b) ₹25 (c) ₹189 (d) ₹21
16. 16.₹245 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹196 (b) ₹147 (c) ₹49 (d) ₹98
17. 17.₹280 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹140 (b) ₹245 (c) ₹35 (d) ₹280
18. 18.If 4 kites cost ₹32, how much do 10 kites cost? (a) ₹88 (b) ₹80 (c) ₹38 (d) ₹320
19. 19.If 9 mangoes cost ₹171, how much do 10 mangoes cost? (a) ₹209 (b) ₹172 (c) ₹190 (d) ₹1710
20. 20.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 21 days (d) 45 days
21. 21.6 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 5 days (d) 10 days
22. 22.If 5 notebooks cost ₹70, how much do 9 notebooks cost? (a) ₹74 (b) ₹140 (c) ₹126 (d) ₹630
23. 23.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 18 days (d) 13 days
24. 24.If 4 mangoes cost ₹64, how much do 7 mangoes cost? (a) ₹67 (b) ₹128 (c) ₹448 (d) ₹112
25. 25.If 8 notebooks cost ₹144, how much do 6 notebooks cost? (a) ₹864 (b) ₹108 (c) ₹142 (d) ₹126
26. 26.₹33 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹11 (b) ₹22 (c) ₹33 (d) ₹23
27. 27.If 6 mangoes cost ₹132, how much do 12 mangoes cost? (a) ₹286 (b) ₹138 (c) ₹1584 (d) ₹264
28. 28.8 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 41 days (b) 40 days (c) 10 days (d) 20 days
29. 29.If 2 mangoes cost ₹14, how much do 8 mangoes cost? (a) ₹56 (b) ₹63 (c) ₹20 (d) ₹112
30. 30.If 5 mangoes cost ₹85, how much do 10 mangoes cost? (a) ₹90 (b) ₹850 (c) ₹170 (d) ₹187
31. 31.If 2 notebooks cost ₹46, how much do 7 notebooks cost? (a) ₹161 (b) ₹184 (c) ₹322 (d) ₹51
32. 32.If 6 kites cost ₹18, how much do 2 kites cost? (a) ₹9 (b) ₹36 (c) ₹14 (d) ₹6
33. 33.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 4 days (d) 8 days
34. 34.If 7 kites cost ₹168, how much do 4 kites cost? (a) ₹120 (b) ₹672 (c) ₹96 (d) ₹165
35. 35.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 5 days (d) 4 days
36. 36.If 8 pens cost ₹112, how much do 10 pens cost? (a) ₹1120 (b) ₹140 (c) ₹114 (d) ₹154
37. 37.If 4 mangoes cost ₹28, how much do 2 mangoes cost? (a) ₹26 (b) ₹56 (c) ₹21 (d) ₹14
38. 38.₹481 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹37 (b) ₹333 (c) ₹296 (d) ₹185
39. 39.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 17 days (c) 34 days (d) 33 days
40. 40.If 4 notebooks cost ₹32, how much do 5 notebooks cost? (a) ₹48 (b) ₹160 (c) ₹40 (d) ₹33

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