Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 284 · 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.₹78 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹24 (b) ₹6 (c) ₹54 (d) ₹39
2. 2.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 28 days (b) 18 days (c) 10 days (d) 7 days
3. 3.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 27 days (d) 26 days
4. 4.If 6 notebooks cost ₹108, how much do 7 notebooks cost? (a) ₹144 (b) ₹126 (c) ₹756 (d) ₹109
5. 5.If 2 kites cost ₹22, how much do 12 kites cost? (a) ₹32 (b) ₹264 (c) ₹143 (d) ₹132
6. 6.If 2 kites cost ₹30, how much do 11 kites cost? (a) ₹39 (b) ₹180 (c) ₹330 (d) ₹165
7. 7.If 7 pens cost ₹49, how much do 3 pens cost? (a) ₹21 (b) ₹147 (c) ₹28 (d) ₹45
8. 8.If 2 kites cost ₹38, how much do 3 kites cost? (a) ₹114 (b) ₹57 (c) ₹76 (d) ₹39
9. 9.If 7 kites cost ₹42, how much do 8 kites cost? (a) ₹43 (b) ₹54 (c) ₹48 (d) ₹336
10. 10.₹56 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹56 (b) ₹7 (c) ₹49 (d) ₹28
11. 11.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 7 days (c) 40 days (d) 39 days
12. 12.If 8 mangoes cost ₹192, how much do 3 mangoes cost? (a) ₹96 (b) ₹576 (c) ₹72 (d) ₹187
13. 13.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 22 days (c) 21 days (d) 11 days
14. 14.5 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) 4 days (d) 5 days
15. 15.If 8 mangoes cost ₹96, how much do 4 mangoes cost? (a) ₹92 (b) ₹48 (c) ₹384 (d) ₹60
16. 16.₹360 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹360 (b) ₹320 (c) ₹40 (d) ₹180
17. 17.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 28 days (c) 7 days (d) 18 days
18. 18.If 2 notebooks cost ₹32, how much do 6 notebooks cost? (a) ₹192 (b) ₹96 (c) ₹36 (d) ₹112
19. 19.₹350 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹100 (b) ₹175 (c) ₹50 (d) ₹250
20. 20.₹176 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹22 (b) ₹154 (c) ₹176 (d) ₹88
21. 21.₹198 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹162 (b) ₹36 (c) ₹18 (d) ₹99
22. 22.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 2 days (c) 3 days (d) 4 days
23. 23.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 17 days (c) 12 days (d) 4 days
24. 24.If 9 pens cost ₹108, how much do 10 pens cost? (a) ₹1080 (b) ₹132 (c) ₹120 (d) ₹109
25. 25.₹220 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹20 (b) ₹110 (c) ₹120 (d) ₹100
26. 26.If 2 mangoes cost ₹8, how much do 6 mangoes cost? (a) ₹24 (b) ₹48 (c) ₹28 (d) ₹12
27. 27.₹172 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹86 (b) ₹172 (c) ₹129 (d) ₹43
28. 28.If 8 pens cost ₹160, how much do 7 pens cost? (a) ₹159 (b) ₹1120 (c) ₹140 (d) ₹160
29. 29.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 6 days (d) 3 days
30. 30.₹96 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹96 (b) ₹32 (c) ₹48 (d) ₹64
31. 31.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 6 days (d) 3 days
32. 32.If 9 kites cost ₹144, how much do 8 kites cost? (a) ₹128 (b) ₹144 (c) ₹1152 (d) ₹143
33. 33.If 8 mangoes cost ₹120, how much do 12 mangoes cost? (a) ₹180 (b) ₹124 (c) ₹1440 (d) ₹195
34. 34.If 7 notebooks cost ₹105, how much do 5 notebooks cost? (a) ₹90 (b) ₹103 (c) ₹75 (d) ₹525
35. 35.₹441 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹392 (b) ₹343 (c) ₹98 (d) ₹49
36. 36.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 16 days (c) 14 days (d) 20 days
37. 37.If 7 mangoes cost ₹98, how much do 6 mangoes cost? (a) ₹98 (b) ₹588 (c) ₹97 (d) ₹84
38. 38.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 3 days (c) 8 days (d) 4 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) 35 days (b) 11 days (c) 19 days (d) 36 days
40. 40.₹240 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹240 (b) ₹120 (c) ₹24 (d) ₹216

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