Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 743 · 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 pens cost ₹100, how much do 6 pens cost? (a) ₹120 (b) ₹600 (c) ₹140 (d) ₹101
2. 2.If 6 notebooks cost ₹30, how much do 3 notebooks cost? (a) ₹27 (b) ₹90 (c) ₹20 (d) ₹15
3. 3.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 11 days (c) 3 days (d) 22 days
4. 4.8 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 24 days (c) 8 days (d) 16 days
5. 5.₹80 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹40 (b) ₹30 (c) ₹10 (d) ₹50
6. 6.₹88 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹64 (b) ₹24 (c) ₹44 (d) ₹8
7. 7.₹350 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹125 (b) ₹175 (c) ₹225 (d) ₹25
8. 8.₹18 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹6 (b) ₹18 (c) ₹12 (d) ₹9
9. 9.₹532 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹190 (b) ₹38 (c) ₹266 (d) ₹342
10. 10.6 workers can build a wall in 14 days. How many days will 12 workers take, working at the same speed? (a) 8 days (b) 28 days (c) 20 days (d) 7 days
11. 11.If 5 pens cost ₹65, how much do 12 pens cost? (a) ₹169 (b) ₹72 (c) ₹156 (d) ₹780
12. 12.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 15 days (d) 14 days
13. 13.₹243 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹27 (b) ₹135 (c) ₹108 (d) ₹162
14. 14.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 26 days (c) 10 days (d) 16 days
15. 15.₹35 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹20 (b) ₹25 (c) ₹15 (d) ₹5
16. 16.If 6 notebooks cost ₹24, how much do 7 notebooks cost? (a) ₹32 (b) ₹28 (c) ₹168 (d) ₹25
17. 17.If 2 notebooks cost ₹48, how much do 5 notebooks cost? (a) ₹144 (b) ₹51 (c) ₹240 (d) ₹120
18. 18.If 2 pens cost ₹16, how much do 11 pens cost? (a) ₹176 (b) ₹25 (c) ₹96 (d) ₹88
19. 19.₹364 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹130 (b) ₹26 (c) ₹234 (d) ₹182
20. 20.If 7 pens cost ₹133, how much do 5 pens cost? (a) ₹665 (b) ₹131 (c) ₹114 (d) ₹95
21. 21.If 5 pens cost ₹125, how much do 10 pens cost? (a) ₹1250 (b) ₹250 (c) ₹275 (d) ₹130
22. 22.₹182 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹91 (b) ₹117 (c) ₹65 (d) ₹13
23. 23.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 9 days (d) 8 days
24. 24.If 3 mangoes cost ₹45, how much do 8 mangoes cost? (a) ₹135 (b) ₹120 (c) ₹360 (d) ₹50
25. 25.4 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) 6 days (d) 4 days
26. 26.If 5 kites cost ₹125, how much do 3 kites cost? (a) ₹100 (b) ₹123 (c) ₹75 (d) ₹375
27. 27.₹180 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹90 (b) ₹18 (c) ₹162 (d) ₹180
28. 28.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 2 days (c) 12 days (d) 3 days
29. 29.₹132 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹22 (b) ₹66 (c) ₹110 (d) ₹132
30. 30.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 35 days (b) 36 days (c) 11 days (d) 17 days
31. 31.₹441 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹196 (b) ₹49 (c) ₹245 (d) ₹294
32. 32.₹588 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹210 (b) ₹42 (c) ₹294 (d) ₹378
33. 33.6 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 12 days (b) 15 days (c) 11 days (d) 13 days
34. 34.₹192 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹16 (b) ₹112 (c) ₹96 (d) ₹80
35. 35.₹40 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹8 (b) ₹20 (c) ₹32 (d) ₹40
36. 36.₹63 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹9 (b) ₹45 (c) ₹54 (d) ₹18
37. 37.₹56 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹28 (b) ₹7 (c) ₹49 (d) ₹56
38. 38.₹378 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹189 (b) ₹378 (c) ₹42 (d) ₹336
39. 39.₹506 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹253 (b) ₹184 (c) ₹322 (d) ₹46
40. 40.₹312 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹156 (b) ₹96 (c) ₹216 (d) ₹24

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