Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 780 · 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.₹175 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹140 (b) ₹141 (c) ₹35 (d) ₹175
2. 2.₹135 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹135 (b) ₹91 (c) ₹45 (d) ₹90
3. 3.If 2 pens cost ₹16, how much do 10 pens cost? (a) ₹80 (b) ₹24 (c) ₹88 (d) ₹160
4. 4.If 5 pens cost ₹45, how much do 11 pens cost? (a) ₹495 (b) ₹51 (c) ₹108 (d) ₹99
5. 5.If 6 mangoes cost ₹150, how much do 5 mangoes cost? (a) ₹149 (b) ₹750 (c) ₹125 (d) ₹150
6. 6.4 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
7. 7.₹100 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹100 (b) ₹25 (c) ₹75 (d) ₹50
8. 8.If 3 kites cost ₹48, how much do 10 kites cost? (a) ₹176 (b) ₹160 (c) ₹55 (d) ₹480
9. 9.If 8 pens cost ₹64, how much do 7 pens cost? (a) ₹63 (b) ₹64 (c) ₹448 (d) ₹56
10. 10.₹140 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹90 (b) ₹50 (c) ₹70 (d) ₹10
11. 11.₹147 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹63 (b) ₹21 (c) ₹84 (d) ₹105
12. 12.If 7 pens cost ₹70, how much do 3 pens cost? (a) ₹30 (b) ₹40 (c) ₹66 (d) ₹210
13. 13.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 21 days (d) 6 days
14. 14.₹162 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹144 (b) ₹18 (c) ₹81 (d) ₹162
15. 15.If 4 pens cost ₹92, how much do 9 pens cost? (a) ₹207 (b) ₹828 (c) ₹97 (d) ₹230
16. 16.₹243 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹27 (b) ₹54 (c) ₹189 (d) ₹216
17. 17.₹308 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹44 (b) ₹154 (c) ₹132 (d) ₹176
18. 18.If 9 notebooks cost ₹171, how much do 8 notebooks cost? (a) ₹1368 (b) ₹152 (c) ₹171 (d) ₹170
19. 19.6 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 14 days (c) 30 days (d) 31 days
20. 20.₹336 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹168 (b) ₹126 (c) ₹42 (d) ₹210
21. 21.₹279 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹249 (b) ₹31 (c) ₹248 (d) ₹279
22. 22.If 6 notebooks cost ₹132, how much do 4 notebooks cost? (a) ₹528 (b) ₹130 (c) ₹110 (d) ₹88
23. 23.₹117 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹9 (b) ₹90 (c) ₹36 (d) ₹81
24. 24.₹506 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹46 (b) ₹253 (c) ₹230 (d) ₹276
25. 25.If 3 notebooks cost ₹27, how much do 2 notebooks cost? (a) ₹18 (b) ₹26 (c) ₹54 (d) ₹27
26. 26.If 7 kites cost ₹154, how much do 8 kites cost? (a) ₹155 (b) ₹1232 (c) ₹198 (d) ₹176
27. 27.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 7 days (c) 39 days (d) 19 days
28. 28.₹135 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹75 (b) ₹90 (c) ₹15 (d) ₹60
29. 29.₹363 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹33 (b) ₹231 (c) ₹132 (d) ₹264
30. 30.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 5 days (c) 15 days (d) 9 days
31. 31.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 11 days (d) 14 days
32. 32.₹369 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹41 (b) ₹329 (c) ₹328 (d) ₹369
33. 33.₹390 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹117 (b) ₹195 (c) ₹273 (d) ₹39
34. 34.If 6 kites cost ₹54, how much do 7 kites cost? (a) ₹63 (b) ₹72 (c) ₹55 (d) ₹378
35. 35.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 25 days (c) 13 days (d) 17 days
36. 36.₹342 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹342 (b) ₹304 (c) ₹38 (d) ₹171
37. 37.If 3 kites cost ₹54, how much do 6 kites cost? (a) ₹57 (b) ₹126 (c) ₹108 (d) ₹324
38. 38.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 16 days (d) 12 days
39. 39.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 36 days (d) 35 days
40. 40.If 8 kites cost ₹80, how much do 9 kites cost? (a) ₹720 (b) ₹81 (c) ₹90 (d) ₹100

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