Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 846 · 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 8 notebooks cost ₹88, how much do 2 notebooks cost? (a) ₹82 (b) ₹22 (c) ₹176 (d) ₹33
2. 2.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 6 days (d) 7 days
3. 3.If 3 mangoes cost ₹15, how much do 7 mangoes cost? (a) ₹105 (b) ₹40 (c) ₹35 (d) ₹19
4. 4.₹250 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹200 (b) ₹250 (c) ₹50 (d) ₹125
5. 5.₹184 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹46 (b) ₹92 (c) ₹184 (d) ₹138
6. 6.₹370 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹185 (b) ₹37 (c) ₹111 (d) ₹259
7. 7.If 6 pens cost ₹66, how much do 2 pens cost? (a) ₹22 (b) ₹132 (c) ₹33 (d) ₹62
8. 8.9 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 15 days (d) 16 days
9. 9.₹104 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹52 (b) ₹39 (c) ₹13 (d) ₹65
10. 10.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 5 days (c) 3 days (d) 4 days
11. 11.9 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 18 days (d) 8 days
12. 12.₹455 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹350 (b) ₹315 (c) ₹35 (d) ₹140
13. 13.₹176 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹112 (b) ₹64 (c) ₹16 (d) ₹88
14. 14.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 11 days (d) 3 days
15. 15.If 5 pens cost ₹65, how much do 10 pens cost? (a) ₹70 (b) ₹650 (c) ₹130 (d) ₹143
16. 16.3 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) 11 days (d) 3 days
17. 17.If 8 kites cost ₹112, how much do 2 kites cost? (a) ₹42 (b) ₹224 (c) ₹28 (d) ₹106
18. 18.If 3 kites cost ₹69, how much do 12 kites cost? (a) ₹828 (b) ₹276 (c) ₹299 (d) ₹78
19. 19.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 15 days (d) 27 days
20. 20.If 8 pens cost ₹40, how much do 3 pens cost? (a) ₹20 (b) ₹120 (c) ₹15 (d) ₹35
21. 21.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 12 days (b) 2 days (c) 4 days (d) 3 days
22. 22.If 3 kites cost ₹75, how much do 5 kites cost? (a) ₹77 (b) ₹125 (c) ₹375 (d) ₹150
23. 23.₹572 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹176 (b) ₹286 (c) ₹44 (d) ₹396
24. 24.₹300 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹270 (b) ₹300 (c) ₹30 (d) ₹150
25. 25.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 13 days (c) 9 days (d) 7 days
26. 26.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 9 days (d) 7 days
27. 27.If 5 kites cost ₹125, how much do 11 kites cost? (a) ₹300 (b) ₹131 (c) ₹1375 (d) ₹275
28. 28.₹387 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹43 (b) ₹258 (c) ₹172 (d) ₹215
29. 29.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 19 days (c) 12 days (d) 18 days
30. 30.If 6 pens cost ₹78, how much do 10 pens cost? (a) ₹780 (b) ₹130 (c) ₹82 (d) ₹143
31. 31.₹238 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹136 (b) ₹102 (c) ₹34 (d) ₹119
32. 32.If 5 notebooks cost ₹30, how much do 8 notebooks cost? (a) ₹54 (b) ₹240 (c) ₹33 (d) ₹48
33. 33.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 4 days (d) 3 days
34. 34.8 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 25 days (c) 4 days (d) 24 days
35. 35.If 6 mangoes cost ₹138, how much do 8 mangoes cost? (a) ₹184 (b) ₹1104 (c) ₹140 (d) ₹207
36. 36.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹60 (b) ₹84 (c) ₹12 (d) ₹108
37. 37.₹533 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹164 (b) ₹410 (c) ₹41 (d) ₹369
38. 38.If 4 notebooks cost ₹68, how much do 5 notebooks cost? (a) ₹340 (b) ₹102 (c) ₹85 (d) ₹69
39. 39.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 23 days (c) 22 days (d) 14 days
40. 40.If 8 pens cost ₹32, how much do 6 pens cost? (a) ₹24 (b) ₹30 (c) ₹28 (d) ₹192

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