Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 732 · 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. 1.6 workers can build a wall in 14 days. How many days will 12 workers take, working at the same speed? (a) 28 days (b) 20 days (c) 7 days (d) 8 days
2. 2.If 4 notebooks cost ₹28, how much do 8 notebooks cost? (a) ₹63 (b) ₹224 (c) ₹32 (d) ₹56
3. 3.If 8 mangoes cost ₹24, how much do 2 mangoes cost? (a) ₹48 (b) ₹18 (c) ₹9 (d) ₹6
4. 4.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 13 days (c) 29 days (d) 28 days
5. 5.If 9 kites cost ₹126, how much do 7 kites cost? (a) ₹112 (b) ₹124 (c) ₹98 (d) ₹882
6. 6.9 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 7 days (d) 10 days
7. 7.If 3 notebooks cost ₹27, how much do 6 notebooks cost? (a) ₹63 (b) ₹162 (c) ₹30 (d) ₹54
8. 8.If 9 mangoes cost ₹171, how much do 8 mangoes cost? (a) ₹152 (b) ₹170 (c) ₹171 (d) ₹1368
9. 9.If 3 notebooks cost ₹60, how much do 4 notebooks cost? (a) ₹240 (b) ₹100 (c) ₹80 (d) ₹61
10. 10.If 7 kites cost ₹126, how much do 2 kites cost? (a) ₹54 (b) ₹252 (c) ₹121 (d) ₹36
11. 11.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 4 days (d) 13 days
12. 12.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 17 days
13. 13.₹145 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹116 (b) ₹58 (c) ₹29 (d) ₹87
14. 14.If 7 kites cost ₹147, how much do 2 kites cost? (a) ₹142 (b) ₹294 (c) ₹63 (d) ₹42
15. 15.If 9 pens cost ₹135, how much do 10 pens cost? (a) ₹165 (b) ₹136 (c) ₹150 (d) ₹1350
16. 16.₹130 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹50 (b) ₹65 (c) ₹10 (d) ₹80
17. 17.₹144 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹18 (b) ₹144 (c) ₹72 (d) ₹126
18. 18.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 2 days (d) 3 days
19. 19.₹450 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹200 (b) ₹50 (c) ₹250 (d) ₹225
20. 20.₹297 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹33 (b) ₹265 (c) ₹297 (d) ₹264
21. 21.If 9 pens cost ₹72, how much do 6 pens cost? (a) ₹69 (b) ₹432 (c) ₹48 (d) ₹56
22. 22.If 3 notebooks cost ₹66, how much do 7 notebooks cost? (a) ₹462 (b) ₹70 (c) ₹176 (d) ₹154
23. 23.₹81 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹36 (b) ₹54 (c) ₹9 (d) ₹45
24. 24.₹364 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹130 (b) ₹182 (c) ₹234 (d) ₹26
25. 25.If 5 mangoes cost ₹45, how much do 9 mangoes cost? (a) ₹90 (b) ₹405 (c) ₹49 (d) ₹81
26. 26.If 9 mangoes cost ₹108, how much do 10 mangoes cost? (a) ₹1080 (b) ₹109 (c) ₹132 (d) ₹120
27. 27.If 4 pens cost ₹84, how much do 7 pens cost? (a) ₹588 (b) ₹147 (c) ₹87 (d) ₹168
28. 28.₹60 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹24 (b) ₹36 (c) ₹12 (d) ₹30
29. 29.₹351 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹234 (b) ₹156 (c) ₹195 (d) ₹39
30. 30.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 21 days (d) 15 days
31. 31.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 28 days (c) 27 days (d) 15 days
32. 32.9 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 54 days (b) 55 days (c) 19 days (d) 5 days
33. 33.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 15 days (d) 6 days
34. 34.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 17 days (c) 2 days (d) 4 days
35. 35.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 20 days (b) 21 days (c) 16 days (d) 14 days
36. 36.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 17 days (d) 12 days
37. 37.₹99 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹66 (b) ₹67 (c) ₹33 (d) ₹99
38. 38.₹195 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹135 (b) ₹15 (c) ₹120 (d) ₹75
39. 39.₹384 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹192 (b) ₹160 (c) ₹32 (d) ₹224
40. 40.If 3 pens cost ₹51, how much do 10 pens cost? (a) ₹58 (b) ₹187 (c) ₹510 (d) ₹170

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