Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 442 · 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.₹187 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹68 (b) ₹136 (c) ₹17 (d) ₹119
2. 2.If 3 kites cost ₹9, how much do 11 kites cost? (a) ₹17 (b) ₹99 (c) ₹33 (d) ₹36
3. 3.₹150 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹75 (b) ₹150 (c) ₹30 (d) ₹120
4. 4.If 9 notebooks cost ₹63, how much do 2 notebooks cost? (a) ₹56 (b) ₹14 (c) ₹126 (d) ₹21
5. 5.₹160 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹80 (b) ₹48 (c) ₹16 (d) ₹112
6. 6.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 17 days (d) 28 days
7. 7.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 8 days (d) 6 days
8. 8.₹328 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹205 (b) ₹164 (c) ₹41 (d) ₹123
9. 9.₹176 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹154 (b) ₹88 (c) ₹176 (d) ₹22
10. 10.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 16 days (c) 15 days (d) 11 days
11. 11.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 24 days (c) 6 days (d) 8 days
12. 12.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 45 days (b) 21 days (c) 5 days (d) 9 days
13. 13.₹154 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹14 (b) ₹98 (c) ₹77 (d) ₹56
14. 14.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 11 days (c) 27 days (d) 15 days
15. 15.If 2 pens cost ₹38, how much do 10 pens cost? (a) ₹380 (b) ₹209 (c) ₹190 (d) ₹46
16. 16.If 9 kites cost ₹207, how much do 7 kites cost? (a) ₹184 (b) ₹1449 (c) ₹205 (d) ₹161
17. 17.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 25 days (c) 13 days (d) 17 days
18. 18.If 8 notebooks cost ₹40, how much do 9 notebooks cost? (a) ₹41 (b) ₹50 (c) ₹360 (d) ₹45
19. 19.If 2 notebooks cost ₹24, how much do 10 notebooks cost? (a) ₹240 (b) ₹120 (c) ₹132 (d) ₹32
20. 20.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 19 days (b) 16 days (c) 12 days (d) 18 days
21. 21.₹264 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹132 (b) ₹154 (c) ₹22 (d) ₹110
22. 22.If 6 mangoes cost ₹150, how much do 9 mangoes cost? (a) ₹153 (b) ₹250 (c) ₹225 (d) ₹1350
23. 23.₹110 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹80 (b) ₹55 (c) ₹10 (d) ₹30
24. 24.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 37 days (c) 36 days (d) 1 day
25. 25.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 43 days (c) 17 days (d) 42 days
26. 26.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 2 days (c) 10 days (d) 8 days
27. 27.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 12 days (c) 23 days (d) 24 days
28. 28.If 3 kites cost ₹9, how much do 12 kites cost? (a) ₹36 (b) ₹39 (c) ₹18 (d) ₹108
29. 29.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 21 days (b) 13 days (c) 22 days (d) 17 days
30. 30.If 4 notebooks cost ₹68, how much do 6 notebooks cost? (a) ₹408 (b) ₹70 (c) ₹102 (d) ₹119
31. 31.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 3 days (d) 5 days
32. 32.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 10 days (c) 6 days (d) 4 days
33. 33.₹368 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹46 (b) ₹368 (c) ₹322 (d) ₹184
34. 34.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 23 days (d) 22 days
35. 35.₹387 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹43 (b) ₹258 (c) ₹215 (d) ₹172
36. 36.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 22 days (c) 11 days (d) 21 days
37. 37.6 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 8 days (c) 4 days (d) 16 days
38. 38.₹154 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹70 (b) ₹77 (c) ₹14 (d) ₹84
39. 39.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 2 days (d) 4 days
40. 40.₹423 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹94 (b) ₹329 (c) ₹376 (d) ₹47

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