Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 56 · 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 5 mangoes cost ₹35, how much do 8 mangoes cost? (a) ₹56 (b) ₹38 (c) ₹280 (d) ₹63
2. 2.If 6 pens cost ₹66, how much do 4 pens cost? (a) ₹44 (b) ₹64 (c) ₹264 (d) ₹55
3. 3.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 14 days (d) 9 days
4. 4.₹440 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹220 (b) ₹44 (c) ₹396 (d) ₹440
5. 5.If 5 mangoes cost ₹75, how much do 12 mangoes cost? (a) ₹195 (b) ₹900 (c) ₹180 (d) ₹82
6. 6.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 7 days
7. 7.If 6 pens cost ₹78, how much do 11 pens cost? (a) ₹156 (b) ₹858 (c) ₹143 (d) ₹83
8. 8.If 3 mangoes cost ₹57, how much do 12 mangoes cost? (a) ₹684 (b) ₹247 (c) ₹228 (d) ₹66
9. 9.If 5 notebooks cost ₹15, how much do 12 notebooks cost? (a) ₹36 (b) ₹39 (c) ₹180 (d) ₹22
10. 10.₹245 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹49 (b) ₹196 (c) ₹245 (d) ₹197
11. 11.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 20 days (d) 21 days
12. 12.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 7 days (c) 39 days (d) 19 days
13. 13.₹132 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹132 (b) ₹22 (c) ₹110 (d) ₹66
14. 14.If 8 pens cost ₹120, how much do 6 pens cost? (a) ₹90 (b) ₹720 (c) ₹105 (d) ₹118
15. 15.If 2 notebooks cost ₹30, how much do 10 notebooks cost? (a) ₹300 (b) ₹38 (c) ₹150 (d) ₹165
16. 16.If 5 pens cost ₹100, how much do 12 pens cost? (a) ₹107 (b) ₹260 (c) ₹1200 (d) ₹240
17. 17.If 8 mangoes cost ₹32, how much do 12 mangoes cost? (a) ₹48 (b) ₹384 (c) ₹36 (d) ₹52
18. 18.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 6 days (d) 4 days
19. 19.8 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 10 days (d) 9 days
20. 20.If 5 pens cost ₹60, how much do 9 pens cost? (a) ₹120 (b) ₹64 (c) ₹540 (d) ₹108
21. 21.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 12 days (c) 9 days (d) 4 days
22. 22.9 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 9 days (d) 11 days
23. 23.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 7 days (d) 5 days
24. 24.If 7 pens cost ₹56, how much do 6 pens cost? (a) ₹336 (b) ₹56 (c) ₹48 (d) ₹55
25. 25.₹264 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹132 (b) ₹165 (c) ₹99 (d) ₹33
26. 26.₹243 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹27 (b) ₹54 (c) ₹189 (d) ₹216
27. 27.If 3 pens cost ₹9, how much do 10 pens cost? (a) ₹90 (b) ₹33 (c) ₹30 (d) ₹16
28. 28.If 5 pens cost ₹65, how much do 6 pens cost? (a) ₹390 (b) ₹78 (c) ₹91 (d) ₹66
29. 29.If 6 notebooks cost ₹126, how much do 10 notebooks cost? (a) ₹130 (b) ₹1260 (c) ₹231 (d) ₹210
30. 30.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 14 days (d) 5 days
31. 31.If 5 notebooks cost ₹90, how much do 3 notebooks cost? (a) ₹72 (b) ₹54 (c) ₹88 (d) ₹270
32. 32.If 6 pens cost ₹48, how much do 7 pens cost? (a) ₹336 (b) ₹56 (c) ₹49 (d) ₹64
33. 33.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 11 days (d) 16 days
34. 34.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 11 days
35. 35.If 5 pens cost ₹30, how much do 9 pens cost? (a) ₹270 (b) ₹60 (c) ₹54 (d) ₹34
36. 36.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 23 days (b) 22 days (c) 14 days (d) 8 days
37. 37.₹450 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹225 (b) ₹250 (c) ₹50 (d) ₹200
38. 38.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 20 days (c) 14 days (d) 5 days
39. 39.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 64 days (c) 63 days (d) 7 days
40. 40.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 3 days (c) 18 days (d) 2 days

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