Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 836 · 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.If 3 notebooks cost ₹48, how much do 4 notebooks cost? (a) ₹80 (b) ₹49 (c) ₹64 (d) ₹192
2. 2.If 5 notebooks cost ₹90, how much do 6 notebooks cost? (a) ₹108 (b) ₹91 (c) ₹126 (d) ₹540
3. 3.₹506 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹138 (b) ₹46 (c) ₹253 (d) ₹368
4. 4.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 11 days (c) 21 days (d) 19 days
5. 5.₹154 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹66 (b) ₹88 (c) ₹77 (d) ₹22
6. 6.If 3 pens cost ₹33, how much do 4 pens cost? (a) ₹55 (b) ₹34 (c) ₹132 (d) ₹44
7. 7.₹70 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹63 (b) ₹70 (c) ₹35 (d) ₹7
8. 8.If 8 pens cost ₹24, how much do 9 pens cost? (a) ₹216 (b) ₹30 (c) ₹25 (d) ₹27
9. 9.₹70 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹14 (b) ₹56 (c) ₹70 (d) ₹35
10. 10.If 4 mangoes cost ₹100, how much do 5 mangoes cost? (a) ₹101 (b) ₹500 (c) ₹150 (d) ₹125
11. 11.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 11 days (c) 26 days (d) 15 days
12. 12.If 7 pens cost ₹35, how much do 11 pens cost? (a) ₹60 (b) ₹55 (c) ₹39 (d) ₹385
13. 13.If 2 pens cost ₹40, how much do 10 pens cost? (a) ₹220 (b) ₹200 (c) ₹400 (d) ₹48
14. 14.₹176 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹112 (b) ₹16 (c) ₹64 (d) ₹88
15. 15.If 9 notebooks cost ₹27, how much do 4 notebooks cost? (a) ₹108 (b) ₹12 (c) ₹15 (d) ₹22
16. 16.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 13 days (b) 16 days (c) 1 day (d) 2 days
17. 17.₹196 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹28 (b) ₹84 (c) ₹112 (d) ₹98
18. 18.₹112 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹56 (b) ₹16 (c) ₹96 (d) ₹112
19. 19.₹270 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹189 (b) ₹27 (c) ₹81 (d) ₹135
20. 20.If 4 notebooks cost ₹32, how much do 8 notebooks cost? (a) ₹256 (b) ₹64 (c) ₹72 (d) ₹36
21. 21.₹84 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹84 (b) ₹72 (c) ₹12 (d) ₹42
22. 22.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 15 days
23. 23.₹140 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹60 (b) ₹20 (c) ₹80 (d) ₹70
24. 24.₹104 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹8 (b) ₹40 (c) ₹64 (d) ₹52
25. 25.If 9 pens cost ₹54, how much do 3 pens cost? (a) ₹48 (b) ₹24 (c) ₹18 (d) ₹162
26. 26.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 9 days (d) 14 days
27. 27.₹481 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹333 (b) ₹185 (c) ₹37 (d) ₹296
28. 28.If 8 mangoes cost ₹112, how much do 7 mangoes cost? (a) ₹784 (b) ₹111 (c) ₹112 (d) ₹98
29. 29.₹253 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹138 (b) ₹161 (c) ₹23 (d) ₹115
30. 30.If 3 notebooks cost ₹12, how much do 9 notebooks cost? (a) ₹36 (b) ₹108 (c) ₹40 (d) ₹18
31. 31.If 8 mangoes cost ₹96, how much do 6 mangoes cost? (a) ₹94 (b) ₹84 (c) ₹72 (d) ₹576
32. 32.₹253 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹23 (b) ₹184 (c) ₹161 (d) ₹92
33. 33.If 7 pens cost ₹140, how much do 6 pens cost? (a) ₹840 (b) ₹120 (c) ₹139 (d) ₹140
34. 34.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 10 days (c) 16 days (d) 1 day
35. 35.₹336 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹168 (b) ₹120 (c) ₹24 (d) ₹216
36. 36.If 5 mangoes cost ₹50, how much do 10 mangoes cost? (a) ₹55 (b) ₹110 (c) ₹500 (d) ₹100
37. 37.₹180 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹20 (b) ₹90 (c) ₹160 (d) ₹180
38. 38.₹100 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹60 (b) ₹50 (c) ₹40 (d) ₹20
39. 39.6 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 5 days (d) 6 days
40. 40.₹441 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹294 (b) ₹49 (c) ₹196 (d) ₹245

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