Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 278 · 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. 1.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 19 days (c) 20 days (d) 21 days
2. 2.If 3 pens cost ₹48, how much do 5 pens cost? (a) ₹50 (b) ₹96 (c) ₹240 (d) ₹80
3. 3.If 6 mangoes cost ₹30, how much do 5 mangoes cost? (a) ₹29 (b) ₹150 (c) ₹25 (d) ₹30
4. 4.₹270 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹135 (b) ₹81 (c) ₹27 (d) ₹189
5. 5.If 3 mangoes cost ₹18, how much do 6 mangoes cost? (a) ₹21 (b) ₹108 (c) ₹42 (d) ₹36
6. 6.₹261 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹232 (b) ₹29 (c) ₹58 (d) ₹203
7. 7.₹352 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹220 (b) ₹44 (c) ₹176 (d) ₹132
8. 8.If 8 kites cost ₹192, how much do 4 kites cost? (a) ₹96 (b) ₹768 (c) ₹188 (d) ₹120
9. 9.If 8 kites cost ₹32, how much do 10 kites cost? (a) ₹320 (b) ₹34 (c) ₹40 (d) ₹44
10. 10.If 6 pens cost ₹18, how much do 7 pens cost? (a) ₹24 (b) ₹126 (c) ₹21 (d) ₹19
11. 11.If 3 mangoes cost ₹48, how much do 12 mangoes cost? (a) ₹192 (b) ₹208 (c) ₹576 (d) ₹57
12. 12.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 28 days (c) 29 days (d) 3 days
13. 13.If 9 notebooks cost ₹72, how much do 7 notebooks cost? (a) ₹70 (b) ₹64 (c) ₹504 (d) ₹56
14. 14.If 4 kites cost ₹64, how much do 5 kites cost? (a) ₹96 (b) ₹320 (c) ₹80 (d) ₹65
15. 15.₹145 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹87 (b) ₹116 (c) ₹29 (d) ₹58
16. 16.If 3 kites cost ₹33, how much do 4 kites cost? (a) ₹55 (b) ₹44 (c) ₹34 (d) ₹132
17. 17.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 13 days (c) 12 days (d) 9 days
18. 18.If 7 kites cost ₹147, how much do 8 kites cost? (a) ₹1176 (b) ₹148 (c) ₹189 (d) ₹168
19. 19.6 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 14 days (d) 6 days
20. 20.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 57 days (b) 8 days (c) 56 days (d) 20 days
21. 21.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 27 days (d) 4 days
22. 22.If 8 mangoes cost ₹112, how much do 12 mangoes cost? (a) ₹116 (b) ₹1344 (c) ₹182 (d) ₹168
23. 23.₹440 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹200 (b) ₹40 (c) ₹220 (d) ₹240
24. 24.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 23 days (c) 13 days (d) 22 days
25. 25.₹306 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹153 (b) ₹238 (c) ₹68 (d) ₹34
26. 26.If 7 mangoes cost ₹56, how much do 12 mangoes cost? (a) ₹104 (b) ₹96 (c) ₹61 (d) ₹672
27. 27.If 3 mangoes cost ₹36, how much do 10 mangoes cost? (a) ₹360 (b) ₹120 (c) ₹132 (d) ₹43
28. 28.If 4 mangoes cost ₹24, how much do 9 mangoes cost? (a) ₹216 (b) ₹29 (c) ₹54 (d) ₹60
29. 29.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 24 days (c) 23 days (d) 25 days
30. 30.If 8 pens cost ₹96, how much do 2 pens cost? (a) ₹36 (b) ₹192 (c) ₹24 (d) ₹90
31. 31.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 10 days (d) 9 days
32. 32.₹168 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹84 (b) ₹63 (c) ₹21 (d) ₹105
33. 33.If 3 kites cost ₹75, how much do 4 kites cost? (a) ₹300 (b) ₹125 (c) ₹100 (d) ₹76
34. 34.If 3 mangoes cost ₹57, how much do 9 mangoes cost? (a) ₹513 (b) ₹190 (c) ₹63 (d) ₹171
35. 35.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 13 days (c) 22 days (d) 21 days
36. 36.₹176 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹16 (b) ₹88 (c) ₹32 (d) ₹144
37. 37.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 8 days (d) 3 days
38. 38.₹336 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹168 (b) ₹192 (c) ₹48 (d) ₹144
39. 39.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 33 days (c) 5 days (d) 34 days
40. 40.If 4 mangoes cost ₹88, how much do 12 mangoes cost? (a) ₹96 (b) ₹286 (c) ₹1056 (d) ₹264

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