Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 940 · 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.₹528 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹48 (b) ₹264 (c) ₹336 (d) ₹192
2. 2.8 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 18 days (b) 25 days (c) 24 days (d) 12 days
3. 3.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 4 days (d) 10 days
4. 4.9 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 30 days (c) 31 days (d) 16 days
5. 5.If 8 notebooks cost ₹112, how much do 7 notebooks cost? (a) ₹111 (b) ₹98 (c) ₹112 (d) ₹784
6. 6.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 8 days (c) 9 days (d) 15 days
7. 7.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 56 days (b) 8 days (c) 57 days (d) 20 days
8. 8.If 9 notebooks cost ₹126, how much do 10 notebooks cost? (a) ₹140 (b) ₹1260 (c) ₹127 (d) ₹154
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) 11 days (c) 16 days (d) 4 days
10. 10.₹39 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹13 (b) ₹27 (c) ₹39 (d) ₹26
11. 11.If 3 notebooks cost ₹18, how much do 6 notebooks cost? (a) ₹36 (b) ₹42 (c) ₹21 (d) ₹108
12. 12.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 29 days (c) 1 day (d) 28 days
13. 13.₹56 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹28 (b) ₹56 (c) ₹48 (d) ₹8
14. 14.9 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 3 days (c) 45 days (d) 46 days
15. 15.If 7 mangoes cost ₹98, how much do 2 mangoes cost? (a) ₹42 (b) ₹93 (c) ₹28 (d) ₹196
16. 16.₹63 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹27 (b) ₹9 (c) ₹36 (d) ₹45
17. 17.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 12 days (b) 7 days (c) 9 days (d) 8 days
18. 18.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 15 days (d) 14 days
19. 19.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 25 days (c) 24 days (d) 23 days
20. 20.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 21 days (c) 22 days (d) 1 day
21. 21.₹322 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹23 (b) ₹161 (c) ₹207 (d) ₹115
22. 22.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 4 days (d) 19 days
23. 23.If 8 mangoes cost ₹48, how much do 2 mangoes cost? (a) ₹96 (b) ₹42 (c) ₹12 (d) ₹18
24. 24.If 7 mangoes cost ₹105, how much do 11 mangoes cost? (a) ₹1155 (b) ₹165 (c) ₹109 (d) ₹180
25. 25.₹370 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹185 (b) ₹259 (c) ₹111 (d) ₹37
26. 26.If 2 kites cost ₹38, how much do 4 kites cost? (a) ₹95 (b) ₹152 (c) ₹40 (d) ₹76
27. 27.If 7 pens cost ₹35, how much do 8 pens cost? (a) ₹45 (b) ₹36 (c) ₹280 (d) ₹40
28. 28.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 2 days (c) 9 days (d) 8 days
29. 29.If 7 kites cost ₹49, how much do 9 kites cost? (a) ₹441 (b) ₹70 (c) ₹51 (d) ₹63
30. 30.If 9 pens cost ₹90, how much do 10 pens cost? (a) ₹91 (b) ₹100 (c) ₹110 (d) ₹900
31. 31.If 2 notebooks cost ₹6, how much do 6 notebooks cost? (a) ₹18 (b) ₹10 (c) ₹36 (d) ₹21
32. 32.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 48 days (d) 18 days
33. 33.If 4 pens cost ₹72, how much do 5 pens cost? (a) ₹108 (b) ₹90 (c) ₹73 (d) ₹360
34. 34.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 43 days (c) 42 days (d) 18 days
35. 35.₹185 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹37 (b) ₹74 (c) ₹111 (d) ₹148
36. 36.₹280 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹280 (b) ₹40 (c) ₹240 (d) ₹140
37. 37.If 3 notebooks cost ₹69, how much do 2 notebooks cost? (a) ₹69 (b) ₹46 (c) ₹138 (d) ₹68
38. 38.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 20 days (b) 13 days (c) 5 days (d) 7 days
39. 39.If 8 mangoes cost ₹144, how much do 6 mangoes cost? (a) ₹108 (b) ₹864 (c) ₹142 (d) ₹126
40. 40.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 28 days (c) 27 days (d) 19 days

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