Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 238 · 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 6 notebooks cost ₹108, how much do 2 notebooks cost? (a) ₹54 (b) ₹36 (c) ₹216 (d) ₹104
2. 2.If 3 pens cost ₹24, how much do 12 pens cost? (a) ₹104 (b) ₹96 (c) ₹33 (d) ₹288
3. 3.If 3 pens cost ₹12, how much do 9 pens cost? (a) ₹40 (b) ₹36 (c) ₹108 (d) ₹18
4. 4.If 2 mangoes cost ₹28, how much do 6 mangoes cost? (a) ₹84 (b) ₹98 (c) ₹168 (d) ₹32
5. 5.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 12 days
6. 6.If 9 notebooks cost ₹189, how much do 7 notebooks cost? (a) ₹1323 (b) ₹187 (c) ₹147 (d) ₹168
7. 7.If 6 notebooks cost ₹78, how much do 7 notebooks cost? (a) ₹79 (b) ₹104 (c) ₹546 (d) ₹91
8. 8.₹169 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹13 (b) ₹117 (c) ₹65 (d) ₹104
9. 9.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 28 days (b) 11 days (c) 19 days (d) 27 days
10. 10.If 6 notebooks cost ₹120, how much do 12 notebooks cost? (a) ₹126 (b) ₹1440 (c) ₹260 (d) ₹240
11. 11.₹351 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹216 (b) ₹135 (c) ₹27 (d) ₹243
12. 12.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 21 days (b) 9 days (c) 5 days (d) 45 days
13. 13.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 11 days (d) 10 days
14. 14.8 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 8 days (b) 18 days (c) 9 days (d) 16 days
15. 15.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 28 days (d) 18 days
16. 16.₹495 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹180 (b) ₹315 (c) ₹360 (d) ₹45
17. 17.8 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 61 days (b) 9 days (c) 60 days (d) 21 days
18. 18.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 13 days (c) 18 days (d) 11 days
19. 19.₹210 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹105 (b) ₹210 (c) ₹30 (d) ₹180
20. 20.₹120 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹60 (b) ₹20 (c) ₹100 (d) ₹120
21. 21.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 5 days (c) 45 days (d) 11 days
22. 22.If 5 pens cost ₹90, how much do 6 pens cost? (a) ₹540 (b) ₹126 (c) ₹108 (d) ₹91
23. 23.If 4 mangoes cost ₹52, how much do 6 mangoes cost? (a) ₹312 (b) ₹78 (c) ₹91 (d) ₹54
24. 24.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 17 days (c) 6 days (d) 5 days
25. 25.If 2 pens cost ₹28, how much do 4 pens cost? (a) ₹70 (b) ₹112 (c) ₹30 (d) ₹56
26. 26.₹180 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹20 (b) ₹90 (c) ₹180 (d) ₹160
27. 27.₹54 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹36 (b) ₹18 (c) ₹54 (d) ₹27
28. 28.If 6 pens cost ₹96, how much do 3 pens cost? (a) ₹64 (b) ₹48 (c) ₹288 (d) ₹93
29. 29.₹560 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹360 (b) ₹280 (c) ₹40 (d) ₹200
30. 30.If 2 kites cost ₹26, how much do 10 kites cost? (a) ₹34 (b) ₹130 (c) ₹143 (d) ₹260
31. 31.₹117 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹36 (b) ₹81 (c) ₹9 (d) ₹90
32. 32.₹162 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹81 (b) ₹72 (c) ₹18 (d) ₹90
33. 33.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 12 days (b) 10 days (c) 3 days (d) 2 days
34. 34.If 3 notebooks cost ₹39, how much do 9 notebooks cost? (a) ₹130 (b) ₹45 (c) ₹117 (d) ₹351
35. 35.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 8 days (d) 9 days
36. 36.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 32 days (b) 7 days (c) 33 days (d) 17 days
37. 37.If 4 mangoes cost ₹80, how much do 6 mangoes cost? (a) ₹82 (b) ₹480 (c) ₹140 (d) ₹120
38. 38.₹224 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹84 (b) ₹112 (c) ₹140 (d) ₹28
39. 39.If 9 mangoes cost ₹54, how much do 3 mangoes cost? (a) ₹162 (b) ₹48 (c) ₹18 (d) ₹24
40. 40.₹242 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹121 (b) ₹154 (c) ₹22 (d) ₹88

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