Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 849 · 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. 1.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 16 days (d) 11 days
2. 2.If 2 notebooks cost ₹28, how much do 3 notebooks cost? (a) ₹84 (b) ₹56 (c) ₹42 (d) ₹29
3. 3.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 53 days (c) 19 days (d) 52 days
4. 4.₹576 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹240 (b) ₹336 (c) ₹48 (d) ₹288
5. 5.₹224 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹80 (b) ₹144 (c) ₹112 (d) ₹16
6. 6.₹297 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹27 (b) ₹216 (c) ₹108 (d) ₹189
7. 7.₹430 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹43 (b) ₹301 (c) ₹129 (d) ₹215
8. 8.₹132 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹88 (b) ₹44 (c) ₹132 (d) ₹66
9. 9.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 5 days (c) 4 days (d) 6 days
10. 10.If 8 kites cost ₹32, how much do 10 kites cost? (a) ₹40 (b) ₹44 (c) ₹34 (d) ₹320
11. 11.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 7 days (d) 11 days
12. 12.If 5 pens cost ₹25, how much do 6 pens cost? (a) ₹26 (b) ₹150 (c) ₹30 (d) ₹35
13. 13.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 16 days (c) 9 days (d) 15 days
14. 14.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 8 days (d) 1 day
15. 15.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 49 days (c) 19 days (d) 4 days
16. 16.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 8 days (d) 12 days
17. 17.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 21 days (c) 11 days (d) 19 days
18. 18.If 5 notebooks cost ₹25, how much do 12 notebooks cost? (a) ₹32 (b) ₹65 (c) ₹300 (d) ₹60
19. 19.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 11 days (c) 16 days (d) 1 day
20. 20.If 5 notebooks cost ₹35, how much do 11 notebooks cost? (a) ₹84 (b) ₹41 (c) ₹385 (d) ₹77
21. 21.If 2 mangoes cost ₹48, how much do 9 mangoes cost? (a) ₹432 (b) ₹216 (c) ₹240 (d) ₹55
22. 22.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 7 days (c) 40 days (d) 19 days
23. 23.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 9 days (d) 5 days
24. 24.If 2 mangoes cost ₹32, how much do 7 mangoes cost? (a) ₹128 (b) ₹224 (c) ₹37 (d) ₹112
25. 25.₹432 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹48 (b) ₹192 (c) ₹240 (d) ₹216
26. 26.If 9 pens cost ₹36, how much do 2 pens cost? (a) ₹72 (b) ₹29 (c) ₹12 (d) ₹8
27. 27.If 4 notebooks cost ₹72, how much do 12 notebooks cost? (a) ₹234 (b) ₹80 (c) ₹216 (d) ₹864
28. 28.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 11 days
29. 29.If 4 pens cost ₹96, how much do 8 pens cost? (a) ₹216 (b) ₹100 (c) ₹192 (d) ₹768
30. 30.₹286 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹104 (b) ₹182 (c) ₹26 (d) ₹143
31. 31.₹180 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹90 (b) ₹72 (c) ₹36 (d) ₹108
32. 32.₹161 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹23 (b) ₹115 (c) ₹46 (d) ₹138
33. 33.If 4 mangoes cost ₹24, how much do 5 mangoes cost? (a) ₹120 (b) ₹25 (c) ₹30 (d) ₹36
34. 34.₹507 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹195 (b) ₹312 (c) ₹351 (d) ₹39
35. 35.₹408 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹170 (b) ₹34 (c) ₹238 (d) ₹204
36. 36.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 5 days (d) 9 days
37. 37.If 6 pens cost ₹54, how much do 7 pens cost? (a) ₹378 (b) ₹72 (c) ₹55 (d) ₹63
38. 38.If 2 pens cost ₹20, how much do 11 pens cost? (a) ₹220 (b) ₹120 (c) ₹29 (d) ₹110
39. 39.If 2 mangoes cost ₹44, how much do 9 mangoes cost? (a) ₹220 (b) ₹396 (c) ₹198 (d) ₹51
40. 40.If 2 kites cost ₹24, how much do 9 kites cost? (a) ₹216 (b) ₹120 (c) ₹108 (d) ₹31

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