Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 963 · 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 ₹48, how much do 5 pens cost? (a) ₹49 (b) ₹240 (c) ₹72 (d) ₹60
2. 2.₹60 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹30 (b) ₹18 (c) ₹6 (d) ₹42
3. 3.If 3 pens cost ₹30, how much do 4 pens cost? (a) ₹40 (b) ₹50 (c) ₹31 (d) ₹120
4. 4.5 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 30 days (b) 15 days (c) 31 days (d) 9 days
5. 5.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 5 days (c) 44 days (d) 17 days
6. 6.₹143 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹117 (b) ₹104 (c) ₹13 (d) ₹39
7. 7.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 5 days (d) 9 days
8. 8.₹276 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹23 (b) ₹161 (c) ₹138 (d) ₹115
9. 9.6 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 30 days (c) 6 days (d) 31 days
10. 10.If 5 kites cost ₹40, how much do 4 kites cost? (a) ₹40 (b) ₹32 (c) ₹39 (d) ₹160
11. 11.₹250 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹125 (b) ₹50 (c) ₹100 (d) ₹150
12. 12.If 8 pens cost ₹128, how much do 3 pens cost? (a) ₹64 (b) ₹123 (c) ₹384 (d) ₹48
13. 13.If 9 pens cost ₹153, how much do 6 pens cost? (a) ₹150 (b) ₹119 (c) ₹918 (d) ₹102
14. 14.₹169 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹13 (b) ₹117 (c) ₹65 (d) ₹104
15. 15.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 4 days (c) 9 days (d) 7 days
16. 16.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 16 days (c) 3 days (d) 9 days
17. 17.If 9 kites cost ₹216, how much do 4 kites cost? (a) ₹211 (b) ₹120 (c) ₹96 (d) ₹864
18. 18.If 2 pens cost ₹44, how much do 11 pens cost? (a) ₹242 (b) ₹484 (c) ₹53 (d) ₹264
19. 19.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 4 days (c) 6 days (d) 36 days
20. 20.If 9 mangoes cost ₹153, how much do 12 mangoes cost? (a) ₹1836 (b) ₹156 (c) ₹221 (d) ₹204
21. 21.If 7 kites cost ₹147, how much do 4 kites cost? (a) ₹105 (b) ₹84 (c) ₹144 (d) ₹588
22. 22.₹184 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹92 (b) ₹115 (c) ₹23 (d) ₹69
23. 23.₹125 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹25 (b) ₹125 (c) ₹101 (d) ₹100
24. 24.If 5 mangoes cost ₹100, how much do 4 mangoes cost? (a) ₹99 (b) ₹80 (c) ₹100 (d) ₹400
25. 25.₹99 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹88 (b) ₹11 (c) ₹22 (d) ₹77
26. 26.₹319 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹58 (b) ₹290 (c) ₹261 (d) ₹29
27. 27.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 23 days (c) 24 days (d) 25 days
28. 28.₹98 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹49 (b) ₹70 (c) ₹28 (d) ₹14
29. 29.₹172 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹172 (b) ₹86 (c) ₹43 (d) ₹129
30. 30.₹66 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹36 (b) ₹30 (c) ₹33 (d) ₹6
31. 31.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 13 days (c) 3 days (d) 5 days
32. 32.₹238 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹34 (b) ₹119 (c) ₹238 (d) ₹204
33. 33.If 6 kites cost ₹84, how much do 3 kites cost? (a) ₹252 (b) ₹42 (c) ₹56 (d) ₹81
34. 34.If 3 mangoes cost ₹39, how much do 7 mangoes cost? (a) ₹104 (b) ₹43 (c) ₹273 (d) ₹91
35. 35.4 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
36. 36.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 7 days (c) 11 days (d) 16 days
37. 37.If 8 notebooks cost ₹104, how much do 2 notebooks cost? (a) ₹208 (b) ₹26 (c) ₹98 (d) ₹39
38. 38.9 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 1 day (b) 5 days (c) 6 days (d) 7 days
39. 39.If 6 pens cost ₹48, how much do 12 pens cost? (a) ₹576 (b) ₹54 (c) ₹96 (d) ₹104
40. 40.If 6 pens cost ₹42, how much do 4 pens cost? (a) ₹28 (b) ₹35 (c) ₹168 (d) ₹40

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