Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 571 · 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 9 kites cost ₹99, how much do 3 kites cost? (a) ₹297 (b) ₹33 (c) ₹44 (d) ₹93
2. 2.₹374 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹204 (b) ₹187 (c) ₹34 (d) ₹170
3. 3.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 27 days (b) 26 days (c) 9 days (d) 17 days
4. 4.₹286 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹26 (b) ₹156 (c) ₹143 (d) ₹130
5. 5.If 8 kites cost ₹80, how much do 7 kites cost? (a) ₹80 (b) ₹79 (c) ₹560 (d) ₹70
6. 6.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 26 days (b) 16 days (c) 27 days (d) 10 days
7. 7.₹384 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹160 (b) ₹224 (c) ₹192 (d) ₹32
8. 8.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 22 days (c) 21 days (d) 3 days
9. 9.8 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 13 days (c) 6 days (d) 5 days
10. 10.₹232 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹145 (b) ₹116 (c) ₹87 (d) ₹29
11. 11.6 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 12 days (d) 11 days
12. 12.₹189 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹135 (b) ₹81 (c) ₹27 (d) ₹108
13. 13.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 10 days (d) 18 days
14. 14.₹204 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹85 (b) ₹17 (c) ₹102 (d) ₹119
15. 15.If 9 notebooks cost ₹207, how much do 2 notebooks cost? (a) ₹69 (b) ₹46 (c) ₹200 (d) ₹414
16. 16.5 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
17. 17.₹336 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹216 (b) ₹120 (c) ₹168 (d) ₹24
18. 18.₹80 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹10 (b) ₹50 (c) ₹40 (d) ₹30
19. 19.₹96 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹48 (b) ₹32 (c) ₹64 (d) ₹96
20. 20.₹80 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹16 (b) ₹80 (c) ₹40 (d) ₹64
21. 21.If 5 pens cost ₹125, how much do 3 pens cost? (a) ₹100 (b) ₹123 (c) ₹75 (d) ₹375
22. 22.₹539 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹49 (b) ₹98 (c) ₹490 (d) ₹441
23. 23.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 5 days (d) 3 days
24. 24.If 4 pens cost ₹48, how much do 5 pens cost? (a) ₹60 (b) ₹49 (c) ₹240 (d) ₹72
25. 25.6 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 2 days (c) 14 days (d) 4 days
26. 26.₹507 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹39 (b) ₹390 (c) ₹351 (d) ₹156
27. 27.₹400 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹40 (b) ₹400 (c) ₹360 (d) ₹200
28. 28.If 5 notebooks cost ₹35, how much do 10 notebooks cost? (a) ₹77 (b) ₹350 (c) ₹70 (d) ₹40
29. 29.₹192 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹112 (b) ₹80 (c) ₹16 (d) ₹96
30. 30.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 1 day (d) 4 days
31. 31.If 9 mangoes cost ₹126, how much do 5 mangoes cost? (a) ₹70 (b) ₹84 (c) ₹630 (d) ₹122
32. 32.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 14 days (b) 12 days (c) 15 days (d) 8 days
33. 33.5 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 13 days (c) 9 days (d) 11 days
34. 34.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 9 days (d) 4 days
35. 35.If 2 notebooks cost ₹30, how much do 4 notebooks cost? (a) ₹120 (b) ₹75 (c) ₹32 (d) ₹60
36. 36.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 17 days (b) 28 days (c) 7 days (d) 11 days
37. 37.₹60 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹30 (b) ₹6 (c) ₹60 (d) ₹54
38. 38.If 7 mangoes cost ₹42, how much do 3 mangoes cost? (a) ₹24 (b) ₹18 (c) ₹126 (d) ₹38
39. 39.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 19 days (c) 36 days (d) 35 days
40. 40.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 12 days (b) 10 days (c) 16 days (d) 11 days

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