Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 535 · 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. 1.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 10 days (d) 8 days
2. 2.If 8 notebooks cost ₹56, how much do 2 notebooks cost? (a) ₹21 (b) ₹50 (c) ₹112 (d) ₹14
3. 3.₹120 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹60 (b) ₹12 (c) ₹36 (d) ₹84
4. 4.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 36 days (b) 18 days (c) 4 days (d) 6 days
5. 5.If 6 pens cost ₹90, how much do 12 pens cost? (a) ₹180 (b) ₹96 (c) ₹1080 (d) ₹195
6. 6.If 7 mangoes cost ₹28, how much do 3 mangoes cost? (a) ₹24 (b) ₹84 (c) ₹16 (d) ₹12
7. 7.8 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
8. 8.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 9 days (c) 13 days (d) 15 days
9. 9.₹176 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹48 (b) ₹16 (c) ₹128 (d) ₹88
10. 10.If 4 mangoes cost ₹96, how much do 6 mangoes cost? (a) ₹168 (b) ₹98 (c) ₹576 (d) ₹144
11. 11.₹240 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹120 (b) ₹30 (c) ₹90 (d) ₹150
12. 12.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 13 days (b) 6 days (c) 4 days (d) 5 days
13. 13.₹117 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹45 (b) ₹9 (c) ₹72 (d) ₹81
14. 14.₹110 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹110 (b) ₹99 (c) ₹55 (d) ₹11
15. 15.If 8 notebooks cost ₹120, how much do 3 notebooks cost? (a) ₹60 (b) ₹45 (c) ₹360 (d) ₹115
16. 16.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 17 days (c) 6 days (d) 4 days
17. 17.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 43 days (b) 17 days (c) 42 days (d) 7 days
18. 18.If 2 pens cost ₹40, how much do 7 pens cost? (a) ₹140 (b) ₹45 (c) ₹280 (d) ₹160
19. 19.If 7 pens cost ₹56, how much do 9 pens cost? (a) ₹58 (b) ₹80 (c) ₹72 (d) ₹504
20. 20.If 6 notebooks cost ₹120, how much do 2 notebooks cost? (a) ₹40 (b) ₹240 (c) ₹116 (d) ₹60
21. 21.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 13 days (d) 17 days
22. 22.₹75 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹15 (b) ₹45 (c) ₹60 (d) ₹30
23. 23.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 19 days (c) 9 days (d) 28 days
24. 24.₹470 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹47 (b) ₹329 (c) ₹141 (d) ₹235
25. 25.If 4 notebooks cost ₹88, how much do 10 notebooks cost? (a) ₹94 (b) ₹242 (c) ₹880 (d) ₹220
26. 26.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 13 days (d) 25 days
27. 27.8 workers can build a wall in 15 days. How many days will 4 workers take, working at the same speed? (a) 30 days (b) 19 days (c) 11 days (d) 31 days
28. 28.₹252 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹216 (b) ₹252 (c) ₹126 (d) ₹36
29. 29.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 23 days (c) 22 days (d) 8 days
30. 30.If 8 notebooks cost ₹192, how much do 7 notebooks cost? (a) ₹1344 (b) ₹191 (c) ₹192 (d) ₹168
31. 31.8 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 18 days (b) 24 days (c) 25 days (d) 12 days
32. 32.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 20 days (c) 5 days (d) 15 days
33. 33.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 3 days (c) 6 days (d) 48 days
34. 34.If 9 mangoes cost ₹153, how much do 10 mangoes cost? (a) ₹187 (b) ₹170 (c) ₹154 (d) ₹1530
35. 35.8 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 7 days (d) 9 days
36. 36.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 3 days (c) 5 days (d) 4 days
37. 37.3 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
38. 38.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 8 days (d) 1 day
39. 39.₹611 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹47 (b) ₹376 (c) ₹423 (d) ₹235
40. 40.If 4 pens cost ₹100, how much do 9 pens cost? (a) ₹900 (b) ₹105 (c) ₹250 (d) ₹225

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