Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 947 · 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 4 pens cost ₹40, how much do 2 pens cost? (a) ₹38 (b) ₹80 (c) ₹20 (d) ₹30
2. 2.6 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 13 days (b) 6 days (c) 10 days (d) 12 days
3. 3.₹182 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹182 (b) ₹156 (c) ₹26 (d) ₹91
4. 4.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 5 days (d) 6 days
5. 5.If 5 pens cost ₹70, how much do 12 pens cost? (a) ₹840 (b) ₹77 (c) ₹168 (d) ₹182
6. 6.If 9 kites cost ₹27, how much do 10 kites cost? (a) ₹28 (b) ₹30 (c) ₹33 (d) ₹270
7. 7.₹204 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹17 (b) ₹102 (c) ₹85 (d) ₹119
8. 8.If 3 pens cost ₹21, how much do 9 pens cost? (a) ₹70 (b) ₹189 (c) ₹27 (d) ₹63
9. 9.If 4 mangoes cost ₹56, how much do 3 mangoes cost? (a) ₹168 (b) ₹55 (c) ₹56 (d) ₹42
10. 10.If 3 pens cost ₹75, how much do 9 pens cost? (a) ₹250 (b) ₹81 (c) ₹225 (d) ₹675
11. 11.9 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 19 days (c) 54 days (d) 55 days
12. 12.If 3 pens cost ₹57, how much do 8 pens cost? (a) ₹456 (b) ₹171 (c) ₹152 (d) ₹62
13. 13.₹110 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹10 (b) ₹40 (c) ₹55 (d) ₹70
14. 14.₹155 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹62 (b) ₹31 (c) ₹93 (d) ₹124
15. 15.If 2 notebooks cost ₹12, how much do 9 notebooks cost? (a) ₹108 (b) ₹60 (c) ₹19 (d) ₹54
16. 16.₹280 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹280 (b) ₹245 (c) ₹140 (d) ₹35
17. 17.₹168 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹72 (b) ₹24 (c) ₹84 (d) ₹96
18. 18.₹80 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹80 (b) ₹10 (c) ₹70 (d) ₹40
19. 19.If 8 mangoes cost ₹168, how much do 5 mangoes cost? (a) ₹126 (b) ₹105 (c) ₹840 (d) ₹165
20. 20.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 18 days (d) 5 days
21. 21.8 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 12 days (c) 13 days (d) 11 days
22. 22.If 6 mangoes cost ₹96, how much do 8 mangoes cost? (a) ₹144 (b) ₹128 (c) ₹98 (d) ₹768
23. 23.7 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 21 days (b) 15 days (c) 9 days (d) 22 days
24. 24.₹90 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹45 (b) ₹90 (c) ₹80 (d) ₹10
25. 25.If 4 kites cost ₹44, how much do 12 kites cost? (a) ₹132 (b) ₹52 (c) ₹528 (d) ₹143
26. 26.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 1 day (d) 7 days
27. 27.If 6 kites cost ₹48, how much do 11 kites cost? (a) ₹96 (b) ₹528 (c) ₹53 (d) ₹88
28. 28.If 4 kites cost ₹20, how much do 5 kites cost? (a) ₹100 (b) ₹30 (c) ₹25 (d) ₹21
29. 29.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 14 days (c) 3 days (d) 4 days
30. 30.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 7 days (d) 28 days
31. 31.If 7 pens cost ₹126, how much do 6 pens cost? (a) ₹756 (b) ₹125 (c) ₹126 (d) ₹108
32. 32.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 21 days (c) 45 days (d) 9 days
33. 33.If 9 notebooks cost ₹216, how much do 10 notebooks cost? (a) ₹217 (b) ₹264 (c) ₹240 (d) ₹2160
34. 34.₹90 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹20 (b) ₹10 (c) ₹45 (d) ₹70
35. 35.If 9 notebooks cost ₹180, how much do 5 notebooks cost? (a) ₹120 (b) ₹100 (c) ₹176 (d) ₹900
36. 36.₹210 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹105 (b) ₹30 (c) ₹60 (d) ₹150
37. 37.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 24 days (d) 16 days
38. 38.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 14 days (c) 2 days (d) 10 days
39. 39.If 7 pens cost ₹161, how much do 5 pens cost? (a) ₹138 (b) ₹159 (c) ₹115 (d) ₹805
40. 40.If 6 mangoes cost ₹54, how much do 7 mangoes cost? (a) ₹55 (b) ₹72 (c) ₹378 (d) ₹63

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