Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 326 · 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.₹225 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹175 (b) ₹25 (c) ₹200 (d) ₹50
2. 2.₹90 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹60 (b) ₹30 (c) ₹90 (d) ₹45
3. 3.If 5 pens cost ₹80, how much do 3 pens cost? (a) ₹48 (b) ₹78 (c) ₹240 (d) ₹64
4. 4.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 18 days (c) 19 days (d) 2 days
5. 5.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 19 days (c) 49 days (d) 9 days
6. 6.If 7 notebooks cost ₹91, how much do 12 notebooks cost? (a) ₹156 (b) ₹96 (c) ₹169 (d) ₹1092
7. 7.₹481 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹185 (b) ₹37 (c) ₹333 (d) ₹296
8. 8.₹468 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹195 (b) ₹234 (c) ₹39 (d) ₹273
9. 9.8 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 4 days (c) 24 days (d) 25 days
10. 10.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 2 days (c) 1 day (d) 3 days
11. 11.If 2 pens cost ₹8, how much do 5 pens cost? (a) ₹24 (b) ₹40 (c) ₹20 (d) ₹11
12. 12.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 19 days (d) 18 days
13. 13.₹117 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹9 (b) ₹81 (c) ₹45 (d) ₹72
14. 14.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 12 days (c) 8 days (d) 5 days
15. 15.If 7 mangoes cost ₹56, how much do 9 mangoes cost? (a) ₹72 (b) ₹58 (c) ₹80 (d) ₹504
16. 16.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 5 days (d) 3 days
17. 17.₹288 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹144 (b) ₹252 (c) ₹288 (d) ₹36
18. 18.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 18 days (c) 19 days (d) 6 days
19. 19.If 4 mangoes cost ₹60, how much do 12 mangoes cost? (a) ₹195 (b) ₹720 (c) ₹68 (d) ₹180
20. 20.If 2 mangoes cost ₹22, how much do 5 mangoes cost? (a) ₹66 (b) ₹110 (c) ₹55 (d) ₹25
21. 21.If 3 notebooks cost ₹21, how much do 4 notebooks cost? (a) ₹35 (b) ₹28 (c) ₹22 (d) ₹84
22. 22.₹126 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹63 (b) ₹42 (c) ₹84 (d) ₹126
23. 23.If 6 mangoes cost ₹66, how much do 8 mangoes cost? (a) ₹528 (b) ₹68 (c) ₹99 (d) ₹88
24. 24.If 2 pens cost ₹26, how much do 4 pens cost? (a) ₹104 (b) ₹28 (c) ₹65 (d) ₹52
25. 25.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 39 days (d) 40 days
26. 26.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 19 days (c) 3 days (d) 4 days
27. 27.₹27 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹9 (b) ₹19 (c) ₹27 (d) ₹18
28. 28.₹209 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹114 (b) ₹133 (c) ₹95 (d) ₹19
29. 29.If 2 mangoes cost ₹22, how much do 6 mangoes cost? (a) ₹77 (b) ₹26 (c) ₹66 (d) ₹132
30. 30.₹72 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹36 (b) ₹6 (c) ₹30 (d) ₹42
31. 31.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 15 days (d) 14 days
32. 32.If 3 kites cost ₹36, how much do 4 kites cost? (a) ₹60 (b) ₹144 (c) ₹37 (d) ₹48
33. 33.If 7 notebooks cost ₹147, how much do 4 notebooks cost? (a) ₹588 (b) ₹84 (c) ₹144 (d) ₹105
34. 34.If 5 mangoes cost ₹45, how much do 3 mangoes cost? (a) ₹135 (b) ₹27 (c) ₹36 (d) ₹43
35. 35.If 6 notebooks cost ₹18, how much do 12 notebooks cost? (a) ₹24 (b) ₹216 (c) ₹39 (d) ₹36
36. 36.If 8 notebooks cost ₹184, how much do 5 notebooks cost? (a) ₹115 (b) ₹920 (c) ₹181 (d) ₹138
37. 37.If 5 kites cost ₹85, how much do 2 kites cost? (a) ₹170 (b) ₹82 (c) ₹34 (d) ₹51
38. 38.If 2 pens cost ₹30, how much do 8 pens cost? (a) ₹135 (b) ₹36 (c) ₹240 (d) ₹120
39. 39.If 9 kites cost ₹108, how much do 8 kites cost? (a) ₹864 (b) ₹108 (c) ₹96 (d) ₹107
40. 40.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 10 days (d) 13 days

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