Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 877 · 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.₹448 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹32 (b) ₹160 (c) ₹224 (d) ₹288
2. 2.₹602 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹301 (b) ₹387 (c) ₹215 (d) ₹43
3. 3.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 25 days (b) 9 days (c) 17 days (d) 13 days
4. 4.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 20 days (b) 6 days (c) 15 days (d) 5 days
5. 5.If 8 mangoes cost ₹112, how much do 12 mangoes cost? (a) ₹1344 (b) ₹116 (c) ₹182 (d) ₹168
6. 6.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 17 days (c) 16 days (d) 1 day
7. 7.₹70 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹35 (b) ₹25 (c) ₹5 (d) ₹45
8. 8.₹64 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹32 (b) ₹56 (c) ₹8 (d) ₹64
9. 9.If 7 pens cost ₹84, how much do 8 pens cost? (a) ₹672 (b) ₹96 (c) ₹108 (d) ₹85
10. 10.If 9 kites cost ₹108, how much do 5 kites cost? (a) ₹540 (b) ₹104 (c) ₹72 (d) ₹60
11. 11.₹429 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹273 (b) ₹234 (c) ₹195 (d) ₹39
12. 12.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 9 days
13. 13.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 4 days (d) 6 days
14. 14.₹189 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹162 (b) ₹189 (c) ₹163 (d) ₹27
15. 15.If 5 notebooks cost ₹110, how much do 2 notebooks cost? (a) ₹107 (b) ₹220 (c) ₹44 (d) ₹66
16. 16.If 6 pens cost ₹114, how much do 7 pens cost? (a) ₹133 (b) ₹152 (c) ₹798 (d) ₹115
17. 17.If 2 pens cost ₹26, how much do 6 pens cost? (a) ₹78 (b) ₹30 (c) ₹91 (d) ₹156
18. 18.₹32 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹16 (b) ₹24 (c) ₹8 (d) ₹32
19. 19.9 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 18 days (b) 14 days (c) 6 days (d) 19 days
20. 20.If 2 kites cost ₹46, how much do 5 kites cost? (a) ₹138 (b) ₹230 (c) ₹49 (d) ₹115
21. 21.If 7 mangoes cost ₹70, how much do 3 mangoes cost? (a) ₹210 (b) ₹66 (c) ₹40 (d) ₹30
22. 22.If 5 kites cost ₹25, how much do 4 kites cost? (a) ₹20 (b) ₹25 (c) ₹24 (d) ₹100
23. 23.If 7 notebooks cost ₹154, how much do 2 notebooks cost? (a) ₹308 (b) ₹44 (c) ₹66 (d) ₹149
24. 24.₹63 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹21 (b) ₹43 (c) ₹63 (d) ₹42
25. 25.If 3 notebooks cost ₹9, how much do 9 notebooks cost? (a) ₹30 (b) ₹27 (c) ₹15 (d) ₹81
26. 26.If 6 notebooks cost ₹54, how much do 4 notebooks cost? (a) ₹36 (b) ₹45 (c) ₹52 (d) ₹216
27. 27.₹576 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹336 (b) ₹48 (c) ₹240 (d) ₹288
28. 28.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 4 days (d) 6 days
29. 29.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 11 days (d) 4 days
30. 30.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 12 days (c) 10 days (d) 11 days
31. 31.₹121 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹33 (b) ₹99 (c) ₹11 (d) ₹88
32. 32.If 6 mangoes cost ₹36, how much do 11 mangoes cost? (a) ₹66 (b) ₹396 (c) ₹41 (d) ₹72
33. 33.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 3 days (d) 4 days
34. 34.If 8 kites cost ₹200, how much do 3 kites cost? (a) ₹195 (b) ₹100 (c) ₹75 (d) ₹600
35. 35.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 19 days (c) 18 days (d) 12 days
36. 36.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 23 days (c) 13 days (d) 9 days
37. 37.If 9 kites cost ₹207, how much do 7 kites cost? (a) ₹184 (b) ₹205 (c) ₹1449 (d) ₹161
38. 38.If 4 pens cost ₹72, how much do 10 pens cost? (a) ₹78 (b) ₹720 (c) ₹180 (d) ₹198
39. 39.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 4 days (d) 3 days
40. 40.If 3 mangoes cost ₹33, how much do 5 mangoes cost? (a) ₹66 (b) ₹55 (c) ₹165 (d) ₹35

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