Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 939 · 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.₹198 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹18 (b) ₹144 (c) ₹54 (d) ₹99
2. 2.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 16 days (c) 28 days (d) 7 days
3. 3.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 22 days (c) 21 days (d) 13 days
4. 4.If 5 pens cost ₹15, how much do 7 pens cost? (a) ₹105 (b) ₹24 (c) ₹21 (d) ₹17
5. 5.₹72 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹6 (b) ₹36 (c) ₹42 (d) ₹30
6. 6.₹140 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹70 (b) ₹14 (c) ₹42 (d) ₹98
7. 7.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 28 days (c) 27 days (d) 13 days
8. 8.₹60 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹30 (b) ₹5 (c) ₹25 (d) ₹35
9. 9.₹602 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹215 (b) ₹301 (c) ₹43 (d) ₹387
10. 10.If 2 mangoes cost ₹6, how much do 12 mangoes cost? (a) ₹39 (b) ₹36 (c) ₹72 (d) ₹16
11. 11.If 4 notebooks cost ₹60, how much do 10 notebooks cost? (a) ₹165 (b) ₹66 (c) ₹600 (d) ₹150
12. 12.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 8 days (d) 3 days
13. 13.If 9 mangoes cost ₹126, how much do 4 mangoes cost? (a) ₹121 (b) ₹504 (c) ₹56 (d) ₹70
14. 14.₹550 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹50 (b) ₹275 (c) ₹350 (d) ₹200
15. 15.If 5 pens cost ₹20, how much do 4 pens cost? (a) ₹20 (b) ₹19 (c) ₹80 (d) ₹16
16. 16.If 2 kites cost ₹12, how much do 4 kites cost? (a) ₹48 (b) ₹30 (c) ₹24 (d) ₹14
17. 17.₹154 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹154 (b) ₹77 (c) ₹22 (d) ₹132
18. 18.If 3 pens cost ₹39, how much do 2 pens cost? (a) ₹78 (b) ₹38 (c) ₹39 (d) ₹26
19. 19.₹161 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹138 (b) ₹46 (c) ₹23 (d) ₹115
20. 20.If 7 pens cost ₹77, how much do 2 pens cost? (a) ₹33 (b) ₹72 (c) ₹22 (d) ₹154
21. 21.₹132 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹110 (b) ₹22 (c) ₹132 (d) ₹66
22. 22.If 9 notebooks cost ₹207, how much do 4 notebooks cost? (a) ₹828 (b) ₹92 (c) ₹115 (d) ₹202
23. 23.₹99 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹27 (b) ₹9 (c) ₹72 (d) ₹81
24. 24.If 9 mangoes cost ₹72, how much do 10 mangoes cost? (a) ₹88 (b) ₹80 (c) ₹73 (d) ₹720
25. 25.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 15 days
26. 26.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 14 days (d) 15 days
27. 27.₹33 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹22 (b) ₹23 (c) ₹33 (d) ₹11
28. 28.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 21 days (c) 22 days (d) 13 days
29. 29.If 9 mangoes cost ₹27, how much do 7 mangoes cost? (a) ₹25 (b) ₹21 (c) ₹189 (d) ₹24
30. 30.If 6 kites cost ₹66, how much do 7 kites cost? (a) ₹67 (b) ₹77 (c) ₹462 (d) ₹88
31. 31.If 3 pens cost ₹69, how much do 7 pens cost? (a) ₹161 (b) ₹483 (c) ₹184 (d) ₹73
32. 32.₹155 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹124 (b) ₹62 (c) ₹31 (d) ₹93
33. 33.If 7 pens cost ₹168, how much do 2 pens cost? (a) ₹72 (b) ₹163 (c) ₹336 (d) ₹48
34. 34.If 7 mangoes cost ₹98, how much do 6 mangoes cost? (a) ₹98 (b) ₹97 (c) ₹588 (d) ₹84
35. 35.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 22 days (c) 13 days (d) 23 days
36. 36.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 12 days (b) 2 days (c) 3 days (d) 10 days
37. 37.If 2 pens cost ₹12, how much do 6 pens cost? (a) ₹72 (b) ₹16 (c) ₹42 (d) ₹36
38. 38.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 27 days (c) 26 days (d) 16 days
39. 39.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 11 days (c) 16 days (d) 17 days
40. 40.₹18 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹6 (b) ₹9 (c) ₹12 (d) ₹18

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