Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 585 · 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 2 notebooks cost ₹24, how much do 5 notebooks cost? (a) ₹120 (b) ₹72 (c) ₹60 (d) ₹27
2. 2.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 8 days (c) 7 days (d) 6 days
3. 3.If 4 notebooks cost ₹20, how much do 8 notebooks cost? (a) ₹24 (b) ₹160 (c) ₹40 (d) ₹45
4. 4.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 2 days (d) 9 days
5. 5.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 12 days (c) 16 days (d) 4 days
6. 6.If 5 pens cost ₹75, how much do 6 pens cost? (a) ₹450 (b) ₹105 (c) ₹76 (d) ₹90
7. 7.₹390 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹195 (b) ₹270 (c) ₹120 (d) ₹30
8. 8.₹196 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹98 (b) ₹70 (c) ₹126 (d) ₹14
9. 9.If 7 pens cost ₹154, how much do 3 pens cost? (a) ₹462 (b) ₹88 (c) ₹66 (d) ₹150
10. 10.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 2 days (b) 1 day (c) 7 days (d) 8 days
11. 11.6 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 16 days (c) 7 days (d) 6 days
12. 12.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 4 days (d) 12 days
13. 13.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 5 days (c) 35 days (d) 15 days
14. 14.₹45 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹41 (b) ₹45 (c) ₹5 (d) ₹40
15. 15.If 4 pens cost ₹84, how much do 2 pens cost? (a) ₹42 (b) ₹63 (c) ₹82 (d) ₹168
16. 16.₹96 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹96 (b) ₹16 (c) ₹80 (d) ₹48
17. 17.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 9 days
18. 18.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 16 days (c) 7 days (d) 11 days
19. 19.If 8 kites cost ₹56, how much do 10 kites cost? (a) ₹70 (b) ₹560 (c) ₹58 (d) ₹77
20. 20.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 10 days (c) 4 days (d) 6 days
21. 21.₹312 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹156 (b) ₹312 (c) ₹273 (d) ₹39
22. 22.₹160 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹32 (b) ₹160 (c) ₹128 (d) ₹80
23. 23.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 31 days (b) 30 days (c) 13 days (d) 17 days
24. 24.₹374 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹272 (b) ₹102 (c) ₹187 (d) ₹34
25. 25.If 4 notebooks cost ₹60, how much do 6 notebooks cost? (a) ₹62 (b) ₹360 (c) ₹90 (d) ₹105
26. 26.If 8 kites cost ₹80, how much do 3 kites cost? (a) ₹240 (b) ₹75 (c) ₹30 (d) ₹40
27. 27.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 10 days (d) 8 days
28. 28.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 13 days (c) 7 days (d) 4 days
29. 29.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 1 day (d) 12 days
30. 30.If 6 kites cost ₹72, how much do 7 kites cost? (a) ₹96 (b) ₹84 (c) ₹73 (d) ₹504
31. 31.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 24 days (b) 4 days (c) 12 days (d) 25 days
32. 32.₹266 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹38 (b) ₹190 (c) ₹133 (d) ₹76
33. 33.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 3 days (d) 7 days
34. 34.If 7 kites cost ₹21, how much do 10 kites cost? (a) ₹24 (b) ₹30 (c) ₹33 (d) ₹210
35. 35.If 2 pens cost ₹34, how much do 10 pens cost? (a) ₹42 (b) ₹187 (c) ₹170 (d) ₹340
36. 36.If 5 notebooks cost ₹120, how much do 7 notebooks cost? (a) ₹840 (b) ₹192 (c) ₹122 (d) ₹168
37. 37.If 8 notebooks cost ₹64, how much do 2 notebooks cost? (a) ₹24 (b) ₹16 (c) ₹128 (d) ₹58
38. 38.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 6 days (c) 19 days (d) 18 days
39. 39.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 13 days (d) 25 days
40. 40.If 4 mangoes cost ₹80, how much do 12 mangoes cost? (a) ₹960 (b) ₹260 (c) ₹88 (d) ₹240

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